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On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

Francois Caron 1, 2 Pierre del Moral 1, 2 Michele Pace 1 Ba-Ngu Vo 3 
1 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean eld particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject.
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Submitted on : Thursday, September 9, 2010 - 6:49:53 PM
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Francois Caron, Pierre del Moral, Michele Pace, Ba-Ngu Vo. On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering. Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2011, 29 (6), ⟨10.1080/07362994.2011.598797⟩. ⟨inria-00516507⟩

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