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.
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.
