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| HAL: inria-00464130, version 1 |
| DOI: 10.1137/100788987 |
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| SIAM Journal on Control and Optimization 49, 4 (2011) 1766-1792 |
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| Particle approximations of a class of branching distribution flows arising in multi-target tracking |
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| François Caron 1, 2Pierre Del Moral 1, 2 |
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| (2011) |
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| 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. |
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| 1: | ALEA (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université de Bordeaux – CNRS : UMR5251 |
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| 2: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 3: | Dept of Statistics & Dept of Computer Science |
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University of British Columbia |
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| Domain | : | Mathematics/Probability |
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| 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. |
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| inria-00464130, version 1 | |
| http://hal.inria.fr/inria-00464130 | |
| oai:hal.inria.fr:inria-00464130 | |
| From: Francois Caron | |
| Submitted on: Tuesday, 16 March 2010 10:05:36 | |
| Updated on: Wednesday, 9 November 2011 10:37:29 | |
