One-dimensional infinite memory imitation models with noise

Abstract

In this paper we study stochastic process indexed by $\mathbb{Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J. Stat. Phys., 150(6):1017--1029, 2013).

22 pages, 3 figures

References in corpus (3)

• Perfect simulation of infinite range Gibbs measures and coupling with their finite range approximations
• Developments in perfect simulation of Gibbs measures through a new result for the extinction of Galton-Watson-like processes
• Perfect simulation of autoregressive models with infinite memory

Cited by in corpus (1)

• Reduction and classification of higher-order Markov chains