Ergodic property of stable-like Markov chains
A stable-like Markov chain (in discrete time) generalizes the concept of a random walk on the real line with \(\alpha\)-stable increments as follows: the increment laws still have a power-law decay, but with a state-dependent exponent \(\alpha(x)+1\). The author studies sufficient criteria for the transience, recurrence and ergodicity of stable-like Markov chains under certain uniformity conditions on the transition density functions. The proofs are based on the Foster-Lyapunov drift criteria.
scientific article; zbMATH DE number 6598633
scientific article