Particle approximations of a class of branching distribution flows arising in multi-target tracking

Autor: Caron, François, del Moral, Pierre, Doucet, Arnaud, Pace, Michele
Přispěvatelé: Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, University of British Columbia (UBC), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2011
Předmět:
Zdroj: SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (4), pp.1766-1792. ⟨10.1137/100788987⟩
SIAM Journal on Control and Optimization, 2011, 49 (4), pp.1766-1792. ⟨10.1137/100788987⟩
ISSN: 0363-0129
1095-7138
DOI: 10.1137/100788987⟩
Popis: International audience; We design a mean field and interacting particle interpretation of a class of spatial branching intensity models with spontaneous births arising in multiple-target tracking problems. In contrast to traditional Feynman-Kac type particle models, the transitions of these interacting particle systems depend on the current particle approximation of the total mass process. In the first part, we analyze the stability properties and the long time behavior of these spatial branching intensity distribution flows. We study the asymptotic behavior of total mass processes and we provide a series of weak Lipschitz type functional contraction inequalities. In the second part, we study the convergence of the mean field particle approximations of these models. Under some appropriate stability conditions on the exploration transitions, we derive uniform and non asymptotic estimates as well as a sub-gaussian concentration inequality and a functional central limit theorem. The stability analysis and the uniform estimates presented in the present article seem to be the first results of this type for this class of spatial branching models.
Databáze: OpenAIRE
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