Verifiable conditions for the irreducibility and aperiodicity of Markov chains by analyzing underlying deterministic models

摘要

We consider Markov chains that obey the following general non-linear state space model: Phi(k)(+)(1) = F (Phi(k), alpha (Phi(k), U-k+(1))) where the function F is C-1 while alpha is typically discontinuous and {U-k : k is an element of Z(0)} is an independent and identically distributed process. We assume that for all x, the random variable a (x, U-1) admits a density p(x) such that (x, w) bar right arrow p(x) (w) is lower semi-continuous.