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作者：Del Moral, Pierre; Doucet, Arnaud
作者单位：Universite de Bordeaux; University of British Columbia; University of British Columbia; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Inria
摘要：We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolutions depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We deve...
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作者：Simatos, Florian; Tibi, Danielle
作者单位：Inria; Universite Paris Cite
摘要：A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is satisfied, they leave the system. The stability region is identified via a fluid limit approach, and strongly relies on a spatial homogenization property: at the fluid level, customers are instantaneously distributed across the network according to the stat...
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作者：Douc, Randal; Gassiat, Elisabeth; Landelle, Benoit; Moulines, Eric
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Universite Paris Saclay; Thales Group; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：In this paper, the forgetting of the initial distribution for a nonergodic Hidden Markov Models (HMM) is studied. A new set of conditions is proposed to establish the forgetting property of the filter. Both a pathwise and mean convergence of the total variation distance of the filter started from two different initial distributions are obtained. The results are illustrated using a generic nonergodic state-space model for which both pathwise and mean exponential stability is established.
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作者：Chigansky, Pavel; van Handel, Ramon
作者单位：Hebrew University of Jerusalem; Princeton University
摘要：We develop necessary and sufficient conditions for uniqueness of the invariant measure of the filtering process associated to an ergodic hidden Markov model in a finite or countable state space. These results provide a complete solution to a problem posed by Blackwell (1957), and subsume earlier partial results due to Kaijser, Kochman and Reeds. The proofs of our main results are based on the stability theory of nonlinear filters.
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作者：Ivanoff, B. Gail; Merzbach, Ely
作者单位：University of Ottawa; Bar Ilan University
摘要：We generalize the classic change-point problem to a change-set framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the set is defined by maximizing the expected value of a gain function. In the case that the unknown change-set is defined by a locally finite set of incomparable points, we present a sufficient condition for optimal detection of the set using multiparameter martingale techniques. Two examples are discussed.
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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...
