Some moment results about the limit of a martingale related to the supercritical
A Law of Large Numbers for Rescaled Random Difference Equations ∗ (2009)
Robert M. Burton, Herold G. Dehling, Uwe Rösler
Abstract: We study the behaviour of stochastic processes defined as an iterated function system Xn+1 = Xn + af(Xn, Un+1) with initial value X0 = x0 and a stationary ergodic input signal (Un)n≥0 for...
MÜNSTER 1 Maximal φ-Inequalities for Nonnegative Submartingales (2009)
G. Alsmeyer, U. Rösler, Gerold Alsmeyer, ...
Let (Mn)n≥0 be a nonnegative submartingale and M ∗ n def = max0≤k≤n Mk, n ≥ 0 the associated maximal sequence. For nondecreasing convex functions φ:[0,∞)→[0, ∞) with φ(0) = 0...
MÜNSTER A Stochastic Fixed Point Equation ForWeighted Minima and Maxima (2009)
G. Alsmeyer, U. Rösler, Gerold Alsmeyer, Uwe Rösler
Given any finite or countable collection of real numbers Tj,j ∈ J, we find all solutions F to the stochastic fixed point equation W d = inf j∈J TjWj, where W and the Wj,j ∈ J are independent...
G. Alsmeyer, U. Rösler, ...
Let (Zn)n≥0 be a supercritical Galton-Watson process with finite reproduction mean µ and normalized limit W = limn→ ∞ µ −nZn. Let further φ: [0,∞) → [0, ∞) be a convex differentiable...
Optimal L$^1$-bounds for submartingales (2008)
The optimal function $f$ satisfying $$ \mathbb{E} |\sum_{1}^n X_i | \ge f(\mathrbb{E}|X_1|,...,\mathbb{E}|X_n|) $$ for every martingale $(X_1,X_1+X_2, ...,\sum_{i=1}^n X_i)$ is shown to be given by...
A stochastic fixed point equation for weighted minima and maxima (2008)
Given any finite or countable collection of real numbers $T_j,j\in J$, we find all solutions $F$ to the stochastic fixed point equation \[W\stackrel{\mathrm {d}}{=}\inf_{j\in J}T_jW_j,\] where $W$...
The Rate of Convergence for Weighted Branching Processes (2008)
Uwe Rösler, Valentin Topchii, Vladimir Vatutin
Let the martingale Wn = Zn mn, where Zn is a weighted branching process and m = E � i Ti is the expected sum of the = factors Ti, converge to some limiting random variable W. We give conditions in...
A Stochastic Fixed Point Equation Related to Weighted Branching (2008)
G. Alsmeyer, U. Rösler, Gerold Alsmeyer, Uwe Rösler
For real numbers C, T1, T2,... we find all solutions µ to the stochastic fixed point equation W � j≥1 TjWj + C, where W, W1, W2,... are independent real-valued random variables with distribution...
G. Alsmeyer, U. Rösler, Gerold Alsmeyer, Uwe Rösler
We consider the supercritical bisexual Galton-Watson process (BGWP) with promiscuous mating, that is a branching process which behaves like an ordinary supercritical Galton-Watson process (GWP) as...
G. Alsmeyer, U. Rösler, Gerold Alsmeyer, Uwe Rösler
We consider the supercritical bisexual Galton-Watson process (BGWP) with promiscuous mating, that is a branching process which behaves like an ordinary supercritical Galton-Watson process (GWP) as...
Signed Central Moments of Integer Valued Measures with Decreasing Density (2007)
Signed central ff-moments of integer valued rv with decreasing density are considered. These are all positive if ff 3=2: We state sharp universal bounds on ff depending only on the expectation of the...
Hyperbolic-Concave Functions and Hardy-Littlewood Maximal Functions (2007)
A class of generalized convex functions, the hyperbolic--concave functions, is defined, and used to characterize the collection of Hardy-- Littlewood maximal functions. These maximal functions and...
Convergence Rate for Stable Weighted Branching Processes (2007)
Uwe Rösler, Topchii Valentin, Vladimir Vatutin, Zn To
Let the martingale Wn = m Zn , where Zn is a weighted branching process and m = E T j is the expected sum of the random factors T j , converge to a limiting random variable W . We give conditions in...
The Best Constant in the Topchii-Vatutin-Inequality (2007)
G. Alsmeyer, U. Rösler, For Martingales, ...
Introduction and Result Let (M n ) n#0 be a martingale with increments D n = M n -M n-1 , n 1, and associated absolute maxima M # n = max 0#k#n |M |, 0. Let further 0 be the class of even convex...
Mathematisches Seminar Christian-Albrechts-Universität zu Kiel (2007)
Uwe Rösler, Ludewig-meyn Strasse
On the analysis of stochastic divide and conquer algorithms.
A Stochastic Fixed Point Equation Related to Weighted Branching with Deterministic Weights (2006)
Alsmeyer, Gerold; Inst. Math. Statistics, Dept. Math. And Computer Science, University Of Münster; Gerolda@math.uni-muenster.de, Rösler, Uwe; Math. Seminar, University Of Kiel; Roesler@math.uni-kiel.de
For real numbers $C,T_{1},T_{2},...$ we find all solutions $mu$ to the stochastic fixed point equation $Weqdistsum_{jge 1}T_{j}W_{j}+C$, where $W,W_{1},W_{2},...$ are independent real-valued...
Asymptotic distribution theory for Hoare's selection algorithm (2003)
Introduction Some thirty years ago Hoare (1962) introduced the algorithm QUICKSORT, now a widely applied and well-studied sorting method. A terse description of the algorithm is in Hoare (1961),...
Asexual Versus Promiscuous Bisexual Galton-Watson Processes: The Extinction Probability Ratio (2002)
We consider the supercritical bisexual Galton–Watson process (BGWP) with promiscuous mating, that is, a branching process which behaves like an ordinary supercritical Galton–Watson process (GWP)...
Convergence of the Maximum a Posteriori Path Estimator in Hidden Markov Models (2002)
In a hidden Markov model (HMM) the underlying nite-state Markov chain cannot be observed directly but only by an additional process. We are interested in estimating the unknown path of the Markov...
The Martin entrance boundary of the Galton-Watson process (2002)
G. Alsmeyer, U. Rösler, Gerold Alsmeyer, Uwe Rösler
The paper provides a complete description of the Martin entrance boundary and its minimal elements for a Galton-Watson process (Zn)n≥0. Since this is easily done and known for critical processes,...
A New Ultimate Convex Hull Algorithm in R² (2000)
Uwe Rösler, William Steiger, David Kravitz
We present a very simple algorithm - NEWHULL - to find the convex hull of S = {P 1 , . . . , Pn}, n given points in R 2 . It may be thought of as a variant of Quickhull; however if the hull of S has...
Deterministic in Contrast to Stochastic Modelling (1999)
The first attempt to model a process is often a deterministic setup with differential equations. The existing stochastic influence is suppressed and hopefully negligible. However, sometimes the...
The weighted Branching Process (1999)
Uwe Rösler, Ammerlander Heerstrasse
We present a new approach via a selfsimilar structure to classical probabilistic limit distributions, which appear as limits of sums of independent random variables. We introduce weighted branching...
An L 2 Convergence Theorem For Random Affine Mappings (1999)
An L, Robert M. Burton, Uwe Rösler
We consider the composition of random i.i.d. affine maps of a Hilbert space to itself. We show convergence of the n'th composition in the Wasserstein metric via a contraction argument. The...
Distributions Slanted to the Right (1999)
We solve Problem 234 in Statistica Neerlandica by introducing the concept of slantedness. Distributions with a decreasing Lebesgue density are slanted to the right. This is no longer true for...
The Contraction Method for Recursive Algorithms (1999)
Uwe Rösler, Ludger Rüschendorf
In this paper we give an introduction to the analysis of algorithms by the contraction method. By means of this method several interesting classes of recursions can be analyzed as particular cases of...
A Limit Theorem for "Quicksort" (1999)
Let X n be the number of comparisons needed by the sorting algorithm Quicksort to sort a list of n numbers into their natural ordering. We show that (X n \Gamma E(X n ))=n converges weakly to some...
On the Analysis of Stochastic Divide and Conquer Algorithms. (1999)
Uwe Rösler, Ludewig-meyn Strasse
This paper develops general tools for the analysis of stochastic divide and conquer algorithms. We concentrate on the average performance and the distribution of the duration of the algorithm. In...
We consider the bisexual Galton-Watson process (BGWP) with promiscuous mating, that is, a branching process which behaves like an ordinary Galton-Watson process as long as at least one male is...
More On How To Cut A Cake Fairly (1990)
Introduction How shall a father cut a cake fairly for his n children, who all have their own individual evaluation of cake pieces? (Steinhaus). For two children a well-known rule is: one child cuts,...
Polymerase chain reaction: replication errors and reliability of gene diagnosis (1989)
Krawczak, Michael, Reiss, Jochen, Schmidtke, Jörg, Rösler, Uwe
The impact of replication errors on the reliability of polymerase chain reaction (PCR) data is studied theoretically. Practical applications of our results to RFLP analysis and oligonucleotide...
The antiretroviral activity of APOBEC3 is inhibited by the foamy virus accessory Bet protein
Löchelt, Martin, Romen, Fabian, Bastone, Patrizia, Muckenfuss, Heide, Kirchner, Nadine, Kim, Yong-Boum, ...
Genome hypermutation of different orthoretroviruses by cellular cytidine deaminases of the APOBEC3 family during reverse transcription has recently been observed. Lentiviruses like HIV-1 have...
The antiretroviral activity of APOBEC3 is inhibited by the foamy virus accessory Bet protein
Löchelt, Martin, Romen, Fabian, Bastone, Patrizia, Muckenfuss, Heide, Kirchner, Nadine, Kim, Yong-Boum, ...
Genome hypermutation of different orthoretroviruses by cellular cytidine deaminases of the APOBEC3 family during reverse transcription has recently been observed. Lentiviruses like HIV-1 have...
Denker, Manfred, Puri, Madan L., Rösler, Uwe
A new approach to the asymptotic normality of the multivariate linear rank statistics is provided along with the Berry-Esséen and the Prohorov distance estimates for the remainder term in the...
The best constant in the Topchii-Vatutin inequality for martingales
Consider the class of even convex functions with [phi](0)=0 and concave derivative on (0,[infinity]). Given any [phi]-integrable martingale (Mn)n[greater-or-equal, slanted]0 with increments ,...
Complete Lattices of Probability Measures with Applications to Martingale Theory
The set of probability measures on IR with the stochastic order and the set of right-tail integrable probability measures on IR with the convex order form complete lattices. Connections of these...