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作者：Imhof, LA
作者单位：RWTH Aachen University
摘要：Fudenberg and Harris' stochastic version of the classical replicator dynamics is considered. The behavior of this diffusion process in the presence of an evolutionarily stable strategy is investigated. Moreover, extinction of dominated strategies and stochastic stability of strict Nash equilibria are studied. The general results are illustrated in connection with a discrete war of attrition. A persistence result for the maximum effort strategy is obtained and an explicit expression for the evo...
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作者：Penrose, MD; Sudbury, A
作者单位：University of Bath; Monash University
摘要：We consider random sequential adsorption processes where the initially empty sites of a graph are irreversibly occupied, in random order, either by monomers which block neighboring sites, or by dimers. We also consider a process where initially occupied sites annihilate their neighbors at random times. We verify that these processes are well defined on infinite graphs, and derive forward equations governing joint vacancy/occupation probabilities. Using these, we derive exact formulae for occup...
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作者：Budhiraja, A; Ghosh, AP
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：In this work we study the problem of asymptotically optimal control of a well-known multi-class queuing network, referred to as the crisscross network, in heavy traffic. We consider exponential inter-arrival and service times, linear holding cost and an infinite horizon discounted cost criterion. In a suitable parameter regime, this problem has been studied in detail by Martins, Shreve and Soner [SIAM J. Control Optim. 34 (1996) 21332171] using viscosity solution methods. In this work, using t...
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作者：Strasser, E
作者单位：Technische Universitat Wien
摘要：The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem 2.1, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) 906-925] from diffusion processes to arbitrary continuous semimartingales. The second main result, Theorem 2.4, is a characterization of a weaker notion of no-arbitrage in terms of the existence of supermartingale densities. The pertaining weaker notion of no-arbi...
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作者：Zähle, I; Cox, JT; Durrett, R
作者单位：University of Erlangen Nuremberg; Syracuse University; Cornell University
摘要：This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman's coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to...
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作者：Zwart, B; Borst, S; Debicki, K
作者单位：Eindhoven University of Technology; Centrum Wiskunde & Informatica (CWI); University of Wroclaw
摘要：We investigate the tail asymptotics of the supremum of X(t) + Y(t) - ct, where X = {X(t), t greater than or equal to 0} and Y = {Y(t), t greater than or equal to 0} are two independent stochastic processes. We assume that the process Y has subexponential characteristics and that the process X is more regular in a certain sense than Y. A key issue examined in earlier studies is under what conditions the process X contributes to large values of the supremum only through its average behavior. The...
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作者：Hu, Y; Imkeller, P; Müller, M
作者单位：Universite de Rennes; Humboldt University of Berlin
摘要：We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under these constraints are identified as stochastic processes which usually are supermartingales, and even martingales for particular strategies. These strategies are seen to be opti...
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作者：Zhang, JF
作者单位：University of Southern California
摘要：In this paper we investigate a class of decoupled forward-backward SDEs, where the volatility of the FSDE is degenerate and the terminal value of the BSDE is a discontinuous function of the FSDE. Such an FBSDE is associated with a degenerate parabolic PDE with discontinuous terminal condition. We first establish a Feynman-Kac type representation formula for the spatial derivative of the solution to the PDE. As a consequence, we show that there exists a stopping time tau such that the martingal...
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作者：Aldous, DJ; Bandyopadhyay, A
作者单位：University of California System; University of California Berkeley; University of Minnesota System; University of Minnesota Twin Cities
摘要：In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X-d = g((xi(i), X-i), i >= 1). Here (xi(i)) and g((.)) are given and the X-i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g((.)) is essentially a maximum or minimum function. We draw attention to the theoretical...
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作者：Bousquet-Mélou, M
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider planar lattice walks that start from (0, 0), remain in the first quadrant i, j >= 0, and are made of three types of steps: North-East, West and South. These walks are known to have remarkable enumerative and probabilistic properties: center dot they are counted by nice numbers [Kreweras, Cahiers du B.U.R.O 6 (1965) 5-105], center dot the generating function of these numbers is algebraic [Gessel, J. Statist. Plann. Inference 14 (1986) 49-58], center dot the stationary distribution o...
