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作者：Saloff-Coste, L.; Zuniga, J.
作者单位：Cornell University; Stanford University
摘要：Starting from a given Markov kernel on a finite set V and a bijection g of V, we construct and study a time inhomogeneous Markov chain whose kernel at time n is obtained from K by transport of g(n-1). We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.
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作者：Lemaire, Vincent; Pages, Gilles
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：We propose an unconstrained stochastic approximation method for finding the optimal change of measure (in an a priori parametric family) to reduce the variance of a Monte Carlo simulation. We consider different parametric families based on the Girsanov theorem and the Esscher transform (exponential-tilting). In [Monte Carlo Methods Appl. 10 (2004) 1-24], it described a projected Robbins-Monro procedure to select the parameter minimizing the variance in a multidimensional Gaussian framework. In...
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作者：Haas, Benedicte
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：The subject of this paper is a fragmentation equation with nonconservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the fragmentation rate, we describe the large time behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equation are constructed via nonincreasing self-similar Markov processes that continuously reach 0 in finite tim...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore County; Brown University
摘要：This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if the time before possible entry into service exceeds the patience time. The dynamics of the system is represented in terms of a pair of measure-valued processes, one that keeps track of the waiting times of the customers in queue and the other that keeps trac...
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作者：Bhamidi, Shankar; van der Hofstad, Remco; Hooghiemstra, Gerard
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology; Delft University of Technology
摘要：We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly chosen connected vertices in the network, as well as for the number of edges on the least weight path, the so-called hopcount. We analyze the configuration model with degree power-law exponentt tau > 2, in which the degrees are assumed to be i.i.d. with a tail di...
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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.
