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On a class of discrete generation interacting particle systems. (English) Zbl 0991.60017

Authors’ abstract: The asymptotic behavior of a general class of discrete generation interacting particle systems is discussed. We provide \(\mathbb{L}_p\)-mean error estimates for their empirical measure on path space and present sufficient conditions for uniform convergence of the particle density profiles with respect to the time parameter. Several examples including mean field particle models, genetic schemes and McKean’s Maxwellian gases will also be given. In the context of Feynman-Kac type limiting distributions we also prove central limit theorems and we start a variance comparison for two generic particle approximating models.

MSC:

60F05 Central limit and other weak theorems
60G35 Signal detection and filtering (aspects of stochastic processes)
93E11 Filtering in stochastic control theory
62L20 Stochastic approximation
82C22 Interacting particle systems in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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