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作者：Kabluchko, Zakhar
作者单位：University of Gottingen
摘要：We describe all countable particle systems on R which have the following three properties: independence, Gaussianity and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson point process with intensity measure m and moving independently of each other according to the law of some Gaussian process xi. We classify all pairs (m, xi) generating a stationary particle system, obtaining three families of examples. In the first, trivial family, the m...
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作者：Delong, Lukasz; Imkeller, Peter
作者单位：Warsaw School of Economics; Humboldt University of Berlin
摘要：We deal with backward stochastic differential equations with time delayed generators. In this new type of equation, a generator at time t can depend on the values of a solution in the past, weighted with a time delay function, for instance, of the moving average type. We prove existence and uniqueness of a solution for a sufficiently small time horizon or for a sufficiently small Lipschitz constant of a generator. We give examples of BSDE with time delayed generators that have multiple solutio...
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作者：Schopp, Eva-Maria
作者单位：University of Freiburg
摘要：In this paper we prove a functional limit theorem for the weighted profile of a b-ary tree. For the proof we use classical martingales connected to branching Markov processes and a generalized version of the profile-polynomial martingale. By embedding, choosing weights and a branch factor in a right way, we finally rediscover the profiles of some well-known discrete time trees.
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作者：Kallsen, J.; Muhle-Karbe, J.
作者单位：University of Kiel; University of Vienna
摘要：In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676-713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, have so far only been used to derive general structural results. These apply the duality theory for fr...
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作者：Cox, J. Theodore
作者单位：Syracuse University
摘要：We consider the stepping stone model on the torus of side L in Z(2) in the limit L -> infinity, and study the time it takes two lineages tracing backward in time to coalesce. Our work fills a gap between the finite range migration case of [Ann. Appl. Probab 15 (2005) 671-699] and the long range case of [Genetics 172 (2006) 701-708], where the migration range is a positive fraction of L. We obtain limit theorems for the intermediate case, and verify a conjecture in [Probability Models for DNA S...
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作者：Peled, Ron
作者单位：New York University
摘要：Intuitively, two metric spaces are rough isometric (or quasi-isometric) if their large-scale metric structure is the same, ignoring fine details. This concept has proven fundamental in the geometric study of groups. Abert, and later Szegedy and Benjamini, have posed several probabilistic questions concerning this concept. In this article, we consider one of the simplest of these: are two independent Poisson point processes on the line rough isometric almost surely? Szegedy conjectured that the...
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作者：Kallsen, J.; Muhle-Karbe, J.
作者单位：University of Kiel; University of Vienna
摘要：We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor process.
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作者：de Saporta, Benoite; Dufour, Francois; Gonzalez, Karen
作者单位：Universite de Bordeaux
摘要：We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location-inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable epsilon-optimal stopping time. The paper is illustrated by a numerical example.
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作者：Sezer, Semih Onur
作者单位：Sabanci University
摘要：In the Wiener disorder problem, the drift of a Wiener process changes suddenly at some unknown and unobservable disorder time. The objective is to detect this change as quickly as possible after it happens. Earlier work on the Bayesian formulation of this problem brings optimal (or asymptotically optimal) detection rules assuming that the prior distribution of the change time is given at time zero, and additional information is received by observing the Wiener process only. Here, we consider a...
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作者：Kella, Offer; Yor, Marc
作者单位：Hebrew University of Jerusalem; Sorbonne Universite; Universite Paris Cite
摘要：We give a representation of the solution for a stochastic linear equation of the form X-t = Y-t + integral((0,t]) X-s-dZ(s) where Z is a cadlag semimartingale and Y is a cadlag adapted process with bounded variation on finite intervals. As an application we study the case where Y and -Z are nondecreasing, jointly have stationary increments and the jumps of -Z are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) p...
