The Annals of Applied Probability

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• Coexistence in locally regulated competing populations and survival of branching annihilating random walk AI翻译
  作者：Blath, Jochen; Etheridge, Alison; Meredith, Mark
  作者单位：Technical University of Berlin; University of Oxford
  摘要：We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system models, which do not, at present, incorporate all of the competitive strategies that a population might adopt. The second is a simplification of the first, in which competition is only supposed to act within lattice sites and the total population size within ea...
• Stationary distribution for dioecious branching particle systems with rapid stirring AI翻译
  作者：Yu, Feng
  作者单位：University of Oxford
  摘要：We study dioccious (i.e., two-sex) branching particle system models, where there are two types of particles, modeling the male and female populations, and where birth of new particles requires the presence of both male and female particles. We show that stationary distributions of various dioecious branching particle models are nontrivial under certain conditions, for example, when there is sufficiently fast stirring.
• Translated poisson approximation using exchangeable pair couplings AI翻译
  作者：Roellin, Adrian
  作者单位：University of Zurich
  摘要：It is shown that the method of exchangeable pairs introduced by Stein [Approximate Computation of Expectations (1986) IMS, Hayward, CA] for normal approximation can effectively be used for translated Poisson approximation. Introducing an additional smoothness condition, one can obtain approximation results in total variation and also in a local limit metric. The result is applied, in particular, to the anti-voter model on finite graphs as analyzed by Rinott and Rotar [Ann. Appl. Probab. 7 (199...
• Evolution of discrete populations and the canonical diffusion of adaptive dynamics AI翻译
  作者：Champagnat, Nicolas; Lambert, Amaury
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
  摘要：The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a deterministic ODE describing the evolution of the dominant type, called the canonical equation of adaptive dynamics. Here, in order to include the effect of stochasticity (genetic drift), we consider self-regulated randomly fluctuating populations subject to mu...
• The two-type richardson model with unbounded initial configurations AI翻译
  作者：Deijfen, Maria; Haggstrom, Olle
  作者单位：Stockholm University; Chalmers University of Technology
  摘要：The two-type Richardson model describes the growth of two competing infections on Z(d) and the main question is whether both infection types can simultaneously grow to occupy infinite parts of Z(d). For bounded initial configurations, this has been thoroughly studied. In this paper, an unbounded initial configuration consisting of points x = (x(1),center dot center dot center dot, x(d)) in the hyperplane H = {X epsilon Z(d) : x(1) = 0} is considered. It is shown that, starting from a configura...
• Analysis of top-swap shuffling for genome rearrangements AI翻译
  作者：Bhatnagar, Nayantara; Caputo, Pietro; Tetali, Prasad; Vigoda, Eric
  作者单位：University System of Georgia; Georgia Institute of Technology; Sapienza University Rome; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
  摘要：We study Markov chains which model genome rearrangements. These models are useful for studying the equilibrium distribution of chromosomal lengths, and are used in methods for estimating genomic distances. The primary Markov chain studied in this paper is the top-swap Markov chain. The top-swap chain is a card-shuffling process with n cards divided over k decks, where the cards are ordered within each deck. A transition consists of choosing a random pair of cards, and if the cards lie in diffe...
• Kernel estimation of greek weights by parameter randomization AI翻译
  作者：Elie, Romuald; Fermanian, Jean-David; Touzi, Nizar
  作者单位：Institut Polytechnique de Paris; ENSAE Paris; BNP Paribas; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：Greek weight associated to a parameterized random variable Z(lambda) is a random variable pi such that del lambda E[phi(Z(lambda))] = E[phi(Z(lambda))pi] for any function phi. The importance of the set of Greek weights for the purpose of Monte Carlo simulations has been highlighted in the recent literature. Our main concern in this paper is to devise methods which produce the optimal weight, which is well known to be given by the score, in a general context where the density of Z(lambda) is no...
• Renewals for exponentially increasing lifetimes, with an application to digital search trees AI翻译
  作者：Dennert, Florian; Gruebel, Rudolf
  作者单位：Leibniz University Hannover
  摘要：We show that the number of renewals up to time t exhibits distributional fluctuations as t -> infinity if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the asymptotics of insertion depth in random trees generated by a bit-comparison strategy from uniform input; we also obtain a representation for the resulting family of limit laws along subsequences. Our approach can also be used to obtain rates of convergence.
• On Lerch's transcendent and the Gaussian random walk AI翻译
  作者：Janssen, A. J. E. M.; van Leeuwaarden, J. S. H.
  作者单位：Philips; Philips Research
  摘要：Let X-1, X-2.... be independent variables, each having a normal distribution with negative mean -beta < 0 and variance 1. We consider the partial sums Sn = X-1 + - - - + X-n, with S-0 = 0, and refer to the process {S-n : n >= 0} as the Gaussian random walk. We present explicit expressions for the mean and variance of the maximum M = max{S-n : n > 0}. These expressions are in terms of Taylor series about beta = 0 with coefficients that involve the Riemann zeta function. Our results extend Kingm...
• Limit laws for random vectors with an extreme component AI翻译
  作者：Heffernan, Janet E.; Resnick, Sidney I.
  作者单位：Lancaster University; Cornell University
  摘要：Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the case of asymptotic dependence, but fails to distinguish between exact independence and asymptotic independence. Hidden regular variation addresses this problem by requiring components of the random v...