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Self-interacting Markov chains: Some asymptotics. (English) Zbl 1158.60045

Summary: Guided by the self-interaction mechanisms introduced in [M. Benaim, M. Ledoux and O. Raimond, Probab. Theory Relat. Fields 122, No. 1, 1–41 (2002; Zbl 1042.60060)] and in [P. Del Moral and L. Miclo, Stochastic Anal. Appl. 24, No. 3, 615–660 (2006; Zbl 1093.60068)], we present a more general definition of self-interacting Markov chains (SIMCs) (than in Del Moral and Miclo [loc. cit.] and Benaim et al. [loc. cit.]). We then establish, for particular self-interaction mechanisms, a stability theorem with error estimation, two central limit theorems, two functional central limit theorems, and the large deviation principle.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F10 Large deviations
60F17 Functional limit theorems; invariance principles
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