We start from Feynman`s idea to use negative probabilities to describe the two slit experiment and other quantum interfernce experiments. Formally by using negative probability distributions we can...
Dubischar, Daniel, Gundlach, Volker Matthias, Steinkamp, Oliver, Khrennikov, Andrei
We propose a model based on random dynamical systems (RDS) in information spaces (realized as rings of $p$-adic integers) which supports Buonomano's non-ergodic interpretation of quantum mechanics....
Demystification of quantum entanglement (2009)
Recently a new attempt to go beyond QM was performed in the form of so called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random...
Von Neumann and Luders postulates and quantum information theory (2009)
This note is devoted to some foundational aspects of quantum mechanics (QM) related to quantum information (QI) theory, especially quantum teleportation and ``one way quantum computing.'' We...
Design of an Experiment to Test Quantum Probabilistic Behavior of the Financial market (2009)
The recent crash demonstrated (once again) that the description of the financial market by present financial mathematics cannot be considered as totally satisfactory. We remind that nowadays...
Quantum-like Cognition from Multiplicity of Time Scales in the Brain (2008)
The majority of quantum models of cognition are based on quantum physical reductionism. Since the brain is composed of quantum systems, one might try to use QM (as a physical theory) to describe such...
Complete account of randomness in the EPR-Bohm-Bell experiment (2008)
Avis, David, Fischer, Paul, Hilbert, Astrid, Khrennikov, Andrei
We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional...
On ergodic behavior of $p$-adic dynamical systems (2008)
Gundlach, Matthias, Khrennikov, Andrei, Lindahl, Karl-Olof
Monomial mappings, $x\mapsto x^n$, are topologically transitive and ergodic with respect to Haar measure on the unit circle in the complex plane. In this paper we obtain an anologous result for...
Modern development of quantum technologies based on quantum information theory stimulated analysis of proposed computational, cryptographic and teleportational schemes from the viewpoint of quantum...
Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation...
On the problem of completeness of QM: von Neumann against Einstein, Podolsky, and Rosen (2008)
We performed a comparative analysis of the arguments of Einstein, Podolsky and Rosen -- EPR, 1935 (against the completeness of QM) and the theoretical formalism of QM (due to von Neumann, 1932). We...
This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform...
In this paper we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed. The Bloch's...
We show that the projection postulate plays a crucial role in the discussion on the so called "quantum nonlocality", in particular in the EPR-argument. We stress that the original von Neumann...
Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables? (2008)
The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize...
Learning of p-adic neural networks (2007)
Andrei Khrennikov, Brunello Tirozzi
A p-adic model which describes a large class of neural networks is presented. In this model the states of neurons are described by digits in the canonical expansion of a p-adic number. Thus each...
A model of quantum-like decision-making with applications to psychology and cognitive science (2007)
We consider the following model of decision-making by cognitive systems. We present an algorithm -- quantum-like representation algorithm (QLRA) -- which provides a possibility to represent...
Conte, Elio, Todarello, Orlando, Federici, Antonio, Vitiello, Francesco, Lopane, Michele, Khrennikov, Andrei, ...
We have executed for the first time an experiment on mental observables concluding that there exists equivalence (that is to say, quantum like behavior) between quantum and cognitive entities.Such...
Bell's inequality: Physics meets Probability (2007)
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the...
The importance of probability interference in social science: rationale and experiment (2007)
Khrennikov, Andrei, Haven, Emmanuel
Probability interference is a fundamental characteristic of quantum mechanics. In this paper we attempt to show with the help of some examples, where this fundamental trait of quantum physics can be...
We try to perform geometrization of psychology by representing mental states, , by points of a metric space, . Evolution of ideas is described by dynamical systems in metric mental space. We apply...
In this paper we present quantum-like (QL) representation of the Shafir-Tversky statistical effect. We apply so called contextual approach. The Shafir-Tversky effect is considered as a consequence of...
The Quantum-Like Brain Operating on Subcognitive and Cognitive Time Scales (2007)
We propose a {\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\it quantum} model. By the latter cognition is created by {\it...
Quantum-like Representation of Macroscopic Configurations (2007)
The aim of this paper is to apply a contextual probabilistic model (in the spirit of Mackey, Gudder, Ballentine) to represent and to generalize some results of quantum logic about possible...
Quantum-like Representation of Extensive Form Games: Wine Testing Game (2007)
We consider an application of the mathematical formalism of quantum mechanics (QM) outside physics, namely, to game theory. We present a simple game between macroscopic players, say Alice and Bob (or...
Classical and quantum randomness and the financial market (2007)
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like...
Quantum-like Probabilistic Models outside Physics (2007)
We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This...
Linear Fractional p-Adic and Adelic Dynamical Systems (2006)
Dragovich, Branko, Khrennikov, Andrei, Mihajlovic, Dusan
Using an adelic approach we simultaneously consider real and p-adic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL (2,...
A Mathematician's Viewpoint to Bell's theorem: In Memory of Walter Philipp (2006)
In this paper dedicated to the memory of Walter Philipp, we formalize the rules of classical$\to$ quantum correspondence and perform a rigorous mathematical analysis of the assumptions in Bell's...
A number theoretical observation about the degeneracy of the genetic code (2006)
Khrennikov, Andrei, Nilsson, Marcus
We discuss the similarity of the degeneration structure of the genetic code with a pure number theoretic -- ``divisors code.'' The most interesting thing about our observation is not that there is a...
Chameleon effect, the range of values hypothesis and reproducing the EPR-Bohm correlations (2006)
Accardi, Luigi, Khrennikov, Andrei
We present a detailed analysis of assumptions that J. Bell used to show that local realism contradicts QM. We find that Bell's viewpoint on realism is nonphysical, because it implicitly assume that...
Gene expression from polynomial dynamics in the 2-adic information space (2006)
We perform geometrization of genetics by representing genetic information by points of the 4-adic {\it information space.} By well known theorem of number theory this space can also be represented as...
Khrennikov, Andrei, Adenier, Guillaume, Nieuwenhuizen, Theo M.
This is a transcript of the round table that took place during the conference Quantum Theory: Reconsideration of Foundations - 3, June 2005, Vaxjo, Sweden. There are presented opinions of leading...
We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of {\it mental space} given by a hierarchic $m$-adic tree....
Quantum mechanics for military officers (2006)
We present a trivial probabilistic illustration for representation of quantum mechanics as an algorithm for approximative calculation of averages.
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory...
Conte, Elio, Khrennikov, Andrei, Zbilut, Joseph P.
It is given a preliminary discussion on the ontic nature of quantum states to be intended as potentialities and on the central role of spin to be considered as the basic essence of quantum mechanical...
Adenier, Guillaume, Khrennikov, Andrei
We analyze anomalies in data to test the violation of Bell's inequality for the EPR-Bohm experiment. We found that the experimental correlations for photon polarization have an intriguing property....
Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics (2006)
Khrennikov, Andrei, Volovich, Yaroslav
We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are...
On the problem of hidden variables for quantum field theory (2006)
We show that QFT (as well as QM) is not a complete physical theory. We constructed a classical statistical model inducing quantum field averages. The phase space consists of square integrable...
To quantum mechanics through random fluctuations at the Planck time scale (2006)
We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase...
Nonlinear Schr\"odinger equations from prequantum classical statistical field theory (2006)
We derive some important features of the standard quantum mechanics from a certain classical-like model -- prequantum classical statistical field theory, PCSFT. In this approach correspondence...
Interpretation of Stationary States in Prequantum Classical Statistical Field Theory (2006)
We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory...
p-Adic and Adelic Superanalysis (2005)
Dragovich, Branko, Khrennikov, Andrei
After a brief review of p-adic numbers, adeles and their functions, we consider real, p-adic and adelic superalgebras, superspaces and superanalyses. A concrete illustration is given by means of the...
Quantum nonlocality or nonergodicity? A critical study of Bell's arguments (2005)
We pay attention that through Bell's arguments one can not distinguish quantum nonlocality and nonergodicity. Therefore experimental violations of Bell's inequality can be as well interpreted as...
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian...
Generalized probabilities taking values in non-Archimedean fields and topological groups (2005)
We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing...
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given...
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given...
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given...
An Introduction to Hyperbolic Analysis (2005)
Khrennikov, Andrei, Segre, Gavriel
An introduction to Hyperbolic Analysis is presented.
Quantum mechanics as an approximation of statistical mechanics for classical fields (2005)
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the...
Prequantum classical statistical model with infinite dimensional phase-space (2005)
We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that...
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given...
This preprint contains a detailed Preface to Proceedinngs of the International Conference ``Foundations of Probability and Physics-3'' held in V\"axj\"o, Sweden, 7-12 June 2004; table of contents and...
Generalization of the Critical Volume NTCP Model in the Radiobiology (2005)
Bulinski, Alexander, Khrennikov, Andrei
A generalization of the well known critical volume NTCP model is proposed to take into account dependence of the functional subunits of irradiated organ (or tissue). A new statistical version of the...
Generalization of the Critical Volume NTCP Model in the Radiobiology (2005)
Bulinski, Alexander, Khrennikov, Andrei
A generalization of the well known critical volume NTCP model is proposed to take into account dependence of the functional subunits of irradiated organ (or tissue). A new statistical version of the...
Generalization of the Critical Volume NTCP Model in the Radiobiology (2005)
Bulinski, Alexander, Khrennikov, Andrei
A generalization of the well known critical volume NTCP model is proposed to take into account dependence of the functional subunits of irradiated organ (or tissue). A new statistical version of the...
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given...
Generalization of the Critical Volume NTCP Model in the Radiobiology (2005)
Bulinski, Alexander, Khrennikov, Andrei
A generalization of the well known critical volume NTCP model is proposed to take into account dependence of the functional subunits of irradiated organ (or tissue). A new statistical version of the...
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given...
Generalization of the Critical Volume NTCP Model in the Radiobiology (2005)
Bulinski, Alexander, Khrennikov, Andrei
A generalization of the well known critical volume NTCP model is proposed to take into account dependence of the functional subunits of irradiated organ (or tissue). A new statistical version of the...
There is presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality....
We consider dynamics of financial markets as dynamics of expectations and discuss such a dynamics from the point of view of phenomenological thermodynamics. We describe a financial Carnot cycle and...
Probabilistic pathway representation of cognitive information (2004)
We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of...
On the notion of a macroscopic quantum system (2004)
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It...
$p$-adic discrete dynamical systems and their applications in physics and cognitive sciences (2004)
This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin...
On Markovian behaviour of $p$-adic random dynamical systems (2004)
Albeverio, Sergio, Gundlach, Matthias, Khrennikov, Andrei, Lindahl, Karl-Olof
We study Markovian and non-Markovian behaviour of stochastic processes generated by $p$-adic random dynamical systems. Given a family of $p$-adic monomial random mappings generating a random...
Bell's inequality for conditional probabilities as a test for quantum-like behaviour of mind (2004)
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is...
EPR-Bohm experiment, interference of probabilities, imprecision of time (2004)
We demonstrate that the EPR-Bohm probabilities can be easily obtained in the classical (but contextual) probabilistic framework by using the formula of interference of probabilities. From this point...
V\"axj\"o interpretation-2003: realism of contexts (2004)
We present a new variant of the V\"axj\"o interpretation: contextualistic statistical realistic. Basic ideas of the V\"axj\"o interpretation-2001 are essentially clarified. We also discuss...
How can one find nonlocality in Bohmian mechanics? (2003)
We perform the probabilistic analysis of the pilot wave formalism. From the probabilistic point of view it is not so natural to follow D. Bohm and to consider nonlocal interactions between parts of...
The Contextual Quantization and the Principle of Complementarity of Probabilities (2003)
Khrennikov, Andrei, Kozyrev, Sergei
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
Contextualist viewpoint to Greenberger-Horne-Zeilinger paradox (2003)
We present probabilistic analysis of the Greenberger-Horne-Zeilinger (GHZ) scheme in the contextualist framework, namely under the assumption that distributions of hidden variables depend on settings...
Probabilistic foundations of quantum mechanics and quantum information (2003)
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.
Interference as a statistical consequence of conjecture on time quant (2003)
Khrennikov, Andrei, Volovich, Yaroslav
We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like...
In spite of the very common opinion we show that QM is not complete and that it is possible to create prequantum models providing finer description of physical reality than QM. There exists (at least...
We perform the analysis of probabilistic assumptions of Bell's approach. We emphasize that J. Bell wrote about probability without to specify the concrete axiomatics of probability theory. The...
A Preliminar Evidence of Quantum Like Behavior in Measurements of Mental States (2003)
Conte, Elio, Todarello, Orlando, Federici, Antonio, Vitiello, Francesco, Lopane, Michele, Khrennikov, Andrei
Experimental results presented in this paper supports the hypothesis on quantum-like statistical behaviour of cognitive systems (at least human beings). Our quantum-like approach gives the...
Classical and quantum spaces as rough images of the fundamental prespace (2003)
In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are...
Testing the Fair Sampling Assumption for EPR-Bell Experiments with Polarizer Beamsplitters (2003)
Adenier, Guillaume, Khrennikov, Andrei
In spite of many attempts, no local realistic model seems to be able to reproduce EPR-Bell type correlations, unless non ideal detection is allowed. The low efficiency of detectors in all experiments...
Contextual approach to quantum mechanics and the theory of the fundamental prespace (2003)
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and...
Reconstruction of quantum theory on the basis of the formula of total probability (2003)
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic...
Quantum theory: Reconsideration of foundations (2003)
The purpose of the conference (the fourth in the series of Vaxjo conferences) was to bring together scientists (physicists, mathematicians and philosophers) who are interested in foundations of...
What is really "quantum" in quantum theory? (2003)
By analysing probabilistic foundations of quantum theory we understood that the so called quantum calculus of probabilities (including Born's rule) is not the main distinguishing feature of...
Local Realism, Contextualism and Loopholes in Bell`s Experiments (2002)
Khrennikov, Andrei, Volovich, Igor
It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We...
Local realist (but contextual) derivation of the EPR-Bohm correlations (2002)
The probabilistic structure of quantum mechanics is investigated in the frequency framework. Such an approach can be interpreted as a contextual approach to quantum probabilities. By using rather...
Einstein, Podolsky and Rosen versus Bohm and Bell (2002)
Khrennikov, Andrei, Volovich, Igor
There is an opinion that the Bohm reformulation of the EPR paradox in terms of spin variables is equivalent to the original one. In this note we show that such an opinion is not justified. We apply...
Noncommutative probability in classical systems (2002)
Khrennikov, Andrei, Kozyrev, Sergei
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like...
Nonclassical Total Probability Formula and Quantum Interference of Probabilities (2002)
Bulinski, Alexander, Khrennikov, Andrei
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in...
Brain as quantum-like computer (2002)
We present a contextualist statistical realistic model for quantum-like representations in physics, cognitive science and psychology. We apply this model to describe cognitive experiments to check...
We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to...
We present comparative analysis of Gill-Weihs-Zeilinger-Zukowski arguments directed against Hess-Philipp anti-Bell arguments. In general we support Hess-Philipp viewpoint to the sequence of...
Fundamental Principle for Quantum Theory (2002)
We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that...
On relations between probabilities under quantum and classical measurements (2002)
Khrennikov, Andrei, Loubenets, Elena
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and...
Discrete Time Leads to Quantum-Like Interference of Deterministic Particles (2002)
Khrennikov, Andrei, Volovich, Yaroslav
In this note we demonstrate that a quantum-like interference picture could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey...
V\"axj\"o Interpretation of Quantum Mechanics (2002)
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the...
Contextual viewpoint to quantum stochastics (2001)
We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities...
Dialogue on Classical and Quantum between mathematician and experimenter (2001)
Khrennikov, Andrei, Summhammer, Johann
This dialogue took place at V\"axj\"o, 19 November 2001. The main aim of our meeting in V\"axj\"o was to clarify our viewpoints on foundations of quantum mechanics. The most attractive in our...
Quantum-like formalism for cognitive measurements (2001)
We develop a kind of quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive (in particular, conscious) systems. By using this formalism we could predict...
Interference of probabilities and number field structure of quantum models (2001)
We study the probabilistic consequences of the choice of the basic number field in quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model...
`Quantum probabilities' as context depending probabilities (2001)
We study transformations of conventional (`classical') probabilities induced by context transitions. It is demonstrated that the transition from one complex of conditions to another induces a...
Linear representations of probabilistic transformations induced by context transitions (2001)
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three...
Quantum statistics via perturbation effects of preparation procedures (2001)
We study the following problem: Is it possible to explain the quantum interference of probabilities in the purely corpuscular model for elementary particles? We demonstrate that (by taking into...
Foundations of Probability and Physics, Round table (2001)
We present the summary of the general discussion on the probabilistic foundations of quantum theory that took place during the round table at the Int. Conf. "Foundations of Probability and Physics",...
Hyperbolic quantum mechanics (2000)
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a...
We provide frequency probabilistic analysis of perturbations of physical systems by preparation procedures. We obtained the classification of possible probabilistic transformations connecting input...
We demonstrate the quantum probabilistic rule (which differ from classical Bayes' formula by the cosinus factor) can be obtained on purely classical basis as a consequence of the perturbation effect...
Einstein and Bell, von Mises and Kolmogorov: reality and locality, frequency and probability (2000)
We perform frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was...
Kolmogorov and von Mises viewpoints to the Greenburger-Horne-Zeilinger paradox (2000)
We present comparative probabilistic analysis of the Greenburger-Horne-Zeilinger paradox in the frameworks of Kolmogorov's (measure-theoretical) and von Mises' (frequency) models of the probability...
We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the...
Non-Kolmogorov probability models and modified Bell's inequality (2000)
We analyse the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics, 1933. We...
The Measure-Theoretical Approach to P-Adic Probability Theory (1998)
Andrei Khrennikov, Shinichi Yamada, Arnoud Van Rooij
this paper we develop a p-adic probability formalism based on measure theory of [19]. By probabilistic reasons we use the special case of this measure theory: measures defined on algebras (such...
Nonclassical total probability formula and quantum interference of probabilities
Bulinski, Alexander, Khrennikov, Andrei
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in...
We investigate (as usual) limit behaviour of sums Sn([omega]) of independent equally distributed random variables. However, limits of probabilities are studied with respect to a p-adic metric (where...
We consider dynamics of financial markets as dynamics of expectations and discuss such a dynamics from the point of view of phenomenological thermodynamics. We describe a financial Carnot cycle and...
Classical and quantum randomness and the financial market
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like...