Self-Interacting Markov Chains: Some Asymptotics

Abstract

Guided by the self-interaction mechanisms introduced in Benaim et al. [2] and in [5], we present a more general definition of self-interacting Markov chains (SIMCs) (than in Del Moral and Miclo [5] and Benaim et al. [2]). 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.