Particle approximations of a class of branching distribution flows arising in multi-target tracking
CARON, François
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
DEL MORAL, Pierre
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Leer más >
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
CARON, François
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
DEL MORAL, Pierre
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
< Leer menos
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Idioma
en
Article de revue
Este ítem está publicado en
SIAM Journal on Control and Optimization. 2011, vol. 49, n° 4, p. 1766-1792
Society for Industrial and Applied Mathematics
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
functional central limit theorems
Spatial branching processes
multi-target tracking problems
mean field and interacting particle systems
Feynman-Kac semigroups
uniform estimates w.r.t. time
functional central limit theorems.
Orígen
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