Fleischmann, Klaus, Mytnik, Leonid, Wachtel, Vitali
A H"older regularity index at given points for density states of (alpha,1,beta)-superprocesses with alpha>1+beta is determined. It is shown that this index is strictly greater than the optimal index...
Fleischmann, Klaus, Mytnik, Leonid, Wachtel, Vitali
For 0 < \alpha \leq 2, a super-\alpha-stable motion X in R^d with branching of index 1 + \beta in (1,2) is considered. Fix arbitrary t > 0. If d < \alpha / \beta, a dichotomy for the density function...
Moderate deviations of random walk in random scenery (2008)
Klaus Fleischmann, Klaus Fleischmann, Peter Mörters, Peter Mörters, Vitali Wachtel, Vitali Wachtel
Abstract: We investigate the cumulative scenery process associated with random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy...
Cluster Formation in a Stepping Stone Model With Continuous, Hierarchically Structured Sites (2007)
Steven Evans, Klaus Fleischmann
A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" L'evy processes. This model can be...
STRONG CLUMPING OF SUPER-BROWNIAN MOTION IN A STABLE CATALYTIC MEDIUM (2007)
A. Dawson, Klaus Fleischmann, Peter M Orters
A typical feature of the long time behaviour of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps (or clusters) at spatially rare sites. We...
STRONG CLUMPING OF SUPER-BROWNIAN MOTION IN A STABLE CATALYTIC MEDIUM (2007)
A. Dawson, Klaus Fleischmann, Peter M Orters
A typical feature of the long time behaviour of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps or clusters at spatially rare sites. We describe...
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst (2006)
Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics, Berlin; Fleischm@wias-berlin.de, Mörters, Peter; University Of Bath; Maspm@bath.ac.uk, Wachtel, Vitali; Weierstrass Institute For Applied Analysis And Stochastics, Berlin; Vakhtel@wias-berlin.de
We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in...
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst (2006)
Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics, Berlin; Fleischm@wias-berlin.de, Mörters, Peter; University Of Bath; Maspm@bath.ac.uk, Wachtel, Vitali; Weierstrass Institute For Applied Analysis And Stochastics, Berlin; Vakhtel@wias-berlin.de
We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in...
Fleischmann, Klaus, Mueller, Carl, Vogt, Pascal
In a recent work, Fleischmann and Mueller (2004) showed the existence of a super-Brownian motion in R^d, d=2,3, with extra birth at the origin. Their construction made use of an analytical approach...
Large deviations for sums defined on a Galton-Watson process (2006)
Fleischmann, Klaus, Wachtel, Vitali
In this paper we study the large deviation behavior of sums of i.i.d. random variables X_i defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX_1^2 and...
Moderate deviations for random walk in random scenery (2006)
Fleischmann, Klaus, Morters, Peter, Wachtel, Vitali
We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles...
Critical Galton-Watson processes: The maximum of total progenies within a large window (2006)
Fleischmann, Klaus, Vatutin, Vladimir A., Wachtel, Vitali
Consider a critical Galton-Watson process Z={Z_n: n=0,1,...} of index 1+alpha, alpha in (0,1]. Let S_k(j) denote the sum of the Z_n with n in the window [k,...,k+j), and M_m(j) the maximum of the S_k...
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst (2005)
Fleischmann, Klaus, Moerters, Peter, Wachtel, Vitali
We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in...
Lower deviation probabilities for supercritical Galton-Watson processes (2005)
Fleischmann, Klaus, Wachtel, Vitali
There is a well-known sequence of constants c_n describing the growth of supercritical Galton-Watson processes Z_n. With 'lower deviation probabilities' we refer to P(Z_n=k_n) with k_n=o(c_n) as n...
Trimmed trees and embedded particle systems (2004)
Fleischmann, Klaus, Swart, Jan M.
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of...
Trimmed trees and embedded particle systems (2004)
Fleischmann, Klaus, Swart, Jan M.
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of...
Large deviation principle for the single point catalytic super Brownian motion (2004)
Fleischmann, Klaus, Xiong, Jie
In the single point catalytic super-Brownian motion "particles" branch only if they meet the position of the single point catalyst. If the branching rate tends to zero, the model degenerates to the...
Large scale localization of a spatial version of Neveu's branching process (2004)
Fleischmann, Klaus, Vakhtel, Vitaly
Recently a spatial versions of Neveu's (1992) continuous-state branching process was constructed by Fleischmann and Sturm (2004). This superprocess with infinite mean branching behaves quite...
Competing Species Superprocesses with Infinite Variance (2003)
Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics; Fleischmann@wias-berlin.de, Mytnik, Leonid; Technion - Israel Institute Of Technology; Leonid@ie.technion.ac.il
We study pairs of interacting measure-valued branching processes (superprocesses) with alpha-stable migration and (1+beta)-branching mechanism. The interaction is realized via some killing procedure....
Competing Species Superprocesses with Infinite Variance (2003)
Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics; Fleischmann@wias-berlin.de, Mytnik, Leonid; Technion - Israel Institute Of Technology; Leonid@ie.technion.ac.il
We study pairs of interacting measure-valued branching processes (superprocesses) with alpha-stable migration and (1+beta)-branching mechanism. The interaction is realized via some killing procedure....
Mutually catalytic branching in the plane : uniqueness (2003)
Dawson, Donald A., Fleischmann, Klaus, Mytnik, Leonid, Perkins, Edwin A., Xiong, Jie
Super-Brownian motion with extra birth at one point (2002)
Fleischmann, Klaus, Mueller, Carl
A super-Brownian motion in two and three dimensions is constructed where ``particles'' give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based...
Mutually catalytic branching in the plane: Finite measure states (2002)
Dawson, Donald A., Etheridge, Alison M., Fleischmann, Klaus, Mytnik, Leonid, Perkins, Edwin A., Xiong, Jie
We study a pair of populations in $\mathbb{R}^{2}$ which undergo diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the...
Strong clumping of super-Brownian motion in a stable catalytic medium (2002)
Dawson, Donald A., Fleischmann, Klaus, Mörters, Peter
A typical feature of the long time behavior of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps (or clusters) at spatially rare sites. We describe...
Mutually Catalytic Branching in The Plane: Infinite Measure States (2002)
Dawson, Donald A.; Carleton University; Ddawson@math.carleton.ca, Etheridge, Alison M.; University Of Oxford; Etheridg@stats.ox.ac.uk, Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics; Fleischmann@wias-berlin.de, Mytnik, Leonid; Technion - Israel Institute Of Technology; Leonid@ie.technion.ac.il, Perkins, Edwin A.; The University Of British Columbia; Perkins@math.ubc.ca, Xiong, Jie; University Of Tennessee; Jxiong@math.utk.edu
A two-type infinite-measure-valued population in R^2 is constructed which undergoes diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the...
Mutually Catalytic Branching in The Plane: Infinite Measure States (2002)
Dawson, Donald A.; Carleton University; Ddawson@math.carleton.ca, Etheridge, Alison M.; University Of Oxford; Etheridg@stats.ox.ac.uk, Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics; Fleischmann@wias-berlin.de, Mytnik, Leonid; Technion - Israel Institute Of Technology; Leonid@ie.technion.ac.il, Perkins, Edwin A.; The University Of British Columbia; Perkins@math.ubc.ca, Xiong, Jie; University Of Tennessee; Jxiong@math.utk.edu
A two-type infinite-measure-valued population in R^2 is constructed which undergoes diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the...
The biodiversity of catalytic super-Brownian motion (2000)
Fleischmann, Klaus, Klenke, Achim
In this paper we investigate the structure of the equilibriumstate of three-dimensional catalytic super-Brownian motion where the catalyst is itself a classical super-Brownian motion.We show that the...
Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees (2000)
Donnelly, Peter, Evans, Steven N., Fleischmann, Klaus, Kurtz, Thomas G., Zhou, Xiaowen
Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in...
Finite time extinction of superprocesses with catalysts (2000)
Dawson, Donald A., Fleischmann, Klaus, Mueller, Carl
Consider a catalytic super-Brownian motion $X =X^\Gamma$ with finite variance branching. Here “catalytic ” means that branching of the reactant $X$ is only possible in the presence of some...
Smooth density field of catalytic super-Brownian motion (1999)
Fleischmann, Klaus, Klenke, Achim
Given an (ordinary) super-Brownian motion (SBM) $\varrho$ on $\mathbf{R}^d$ of dimension $d = 2, 3$, we consider a (catalytic) SBM $X^{\varrho}$ on $\mathbf{R}^d$ with "local branching rates"...
Reduced subcritical Galton-Watson processes in a random environment (1999)
Fleischmann, Klaus, Vatutin, Vladimir A.
We study the structure of genealogical trees of reduced subcritical Galton-Watson processes in a random environment assuming that all (randomly varying in time) offspring generating functions are...
Catalytic And Mutually Catalytic Branching (1999)
Donald A. Dawson, Donald A. Dawson, Klaus Fleischmann, Klaus Fleischmann
In this paper we present an overview of recent work on lattice and measure-valued models of catalytic reactions and in particular catalytic branching systems. The main phenomena exhibited by nearly...
Smooth density field of catalytic super-Brownian motion (1999)
Klaus Fleischmann, Achim Klenke, On R
Given an (ordinary) super-Brownian motion (SBM) % on R d of dimension d = 2; 3; we consider a (catalytic) SBM X % on R d with "local branching rates" %s(dx). We show that X % t is...
Smooth density field of catalytic super-Brownian motion (1999)
Klaus Fleischmann, Achim Klenke, On R
Given an (ordinary) super-Brownian motion (SBM) % on R d of dimension d = 2; 3; we consider a (catalytic) SBM X % on R d with "local branching rates" %s(dx). We show that X % t is...
Continuum-sites stepping-stone models, coalescing exhcangeable partitions, and random trees (1998)
Donnelly, Peter, Evans, Steven N., Fleischmann, Klaus, Kurtz, Thomas G., Zhou, Xiaowen
Analogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general Markov process, and the type--space is infinite. Such processes were defined...
Finite time extinction of super-Brownian motions with catalysts (1998)
Dawson, Donald A., Fleischmann, Klaus, Mueller, Carl
Consider a catalytic super-Brownian motion $X=X^\Gamma$ with finite variance branching. Here `catalytic' means that branching of the reactant $X$ is only possible in the presence of some catalyst....
Continuous dependence of a class of superprocesses on branching parameters and applications (1998)
Dawson, Donald A., Fleischmann, Klaus, Leduc, Guillaume
A general class of finite variance critical $(\xi, \Phi, k)$-superprocesses $X$ in a Luzin space $E$ with cadlag right Markov motion process $\xi$, regular local branching mechanism and branching...
Deviations from typical type proportions in critical multitype Galton-Watson processes (1998)
Klaus Fleischmann, Vladimir A. Vatutin
Consider a critical Ktype Galton-Watson process fZ(t) : t = 0; 1; :::g ; and a real vector w = (w 1 ; :::; wK ) ? : It is well-known that under rather general assumptions, \Omega Z(t); w ff := P k Z...
Continuum-sites steppingstone models, coalescing exchangeable partitions, and random (1998)
Peter Donnelly, Steven N. Evans, Klaus Fleischmann, Thomas G. Kurtz, Xiaowen Zhou
Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in...
Klaus Fleischmann, Vladimir A. Vatutin
A dichotomy concerning extinction and survival (even persistence) at late times is established for critical multitype spatially homogeneous branching particle systems in continuous time under natural...
Cluster formation in a stepping-stone model with continuous, hierarchically structured sites (1996)
Evans, Steven N., Fleischmann, Klaus
A stepping-stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" Lévy processes. This model can be understood as a...
Time-Space Analysis of the Cluster-Formation in Interacting Diffusions (1996)
Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics; Fleischmann@wias-berlin.de, Greven, Andreas; Universitat Erlangen-Nurnberg; Greven@mi.uni-erlangen.de
A countable system of linearly interacting diffusions on the interval [0,1], indexed by a hierarchical group is investigated. A particular choice of the interactions guarantees that we are in the...
Time-Space Analysis of the Cluster-Formation in Interacting Diffusions (1996)
Fleischmann, Klaus; Weierstrass Institute For Applied Analysis And Stochastics; Fleischmann@wias-berlin.de, Greven, Andreas; Universitat Erlangen-Nurnberg; Greven@mi.uni-erlangen.de
A countable system of linearly interacting diffusions on the interval [0,1], indexed by a hierarchical group is investigated. A particular choice of the interactions guarantees that we are in the...
Time-Space Analysis of the Cluster-Formation in Interacting Diffusions (1996)
Klaus Fleischmann, Andreas Greven
A countable system of linearly interacting diffusions on the interval [0; 1], indexed by a hierarchical group is investigated. A particular choice of the interactions guarantees that we are in the...
A super-Brownian motion with a locally infinite catalytic mass (1996)
Klaus Fleischmann, Carl Mueller
A super-Brownian motion X in IR with "hyperbolic" branching rate %2(b) = 1=b 2 , b 2 IR; is constructed, which symbolically could be described by the formal stochastic equation dX t = 1 2...
Longtime Behavior of a Branching Process Controlled By Branching Catalysts (1996)
Donald A. Dawson, Klaus Fleischmann
The model under consideration is a catalytic branching model constructed in [DF96], where the catalysts themselves suffer a spatial branching mechanism. Main attention is paid to dimension d = 3: The...
Persistence of a two-dimensional super-Brownian motion in a catalytic medium (1996)
Alison M. Etheridge, Klaus Fleischmann
The super-Brownian motion X % in a super-Brownian medium % constructed in [DF96a] is known to be persistent (no loss of expected mass in the longtime behaviour) in dimensions one ([DF96a]) and three...
Convergence to a non-trivial equilibrium for two-dimensional catalytic super-Brownian motion (1996)
Klaus Fleischmann, Achim Klenke
In contrast to the classical super-Brownian motion (SBM), the SBM (X % t ) t0 in a super-Brownian medium % (constructed in [DF96a]) is known to be persistent in all three dimensions of its...
Reduced subcritical Galton-Watson processes in a random environment (1996)
Klaus Fleischmann, Vladimir A. Vatutin
We study the structure of genealogical trees of reduced subcritical Galton-Watson processes in a random environment assuming that all (in time randomly varying) offspring generating functions are...
Cluster Formation in a Stepping Stone Model With Continuous, Hierarchically Structured Sites (1995)
Steven N. Evans, Klaus Fleischmann
A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" L'evy processes. This model can be...
Time-space analysis of the clusterformation in interacting diffusions (1994)
Klaus Fleischmann, Andreas Greven
E l e c t r o n
Ein verallgemeinerter Erlangscher Bedienungsprozess. (1972)
Jena, Univ., Math.-Naturwiss. Fak., Diss. A, 1972. (Nicht f. d. Austausch.).
Tieftemperatur-Röntgenkristallstrukturuntersuchungen an Natriummethyl-anti-diazotat. (1970)
München, T. U., F. f. allg. Wiss., Diss., 1970 (Nicht f. d. Aust.).
Strong uniqueness for cyclically symbiotic branching diffusions
Dawson, Donald A., Fleischmann, Klaus, Xiong, Jie
A uniqueness problem raised in 2001 for critical cyclically catalytic super-Brownian motions is solved in the simplified space-less case, that is, for cyclically catalytic branching diffusions X....