Lyapunov-type Conditions for Non-strong Ergodicity of Markov Processes

2019/12/19 by Mao, Yong-Hua, Wang, Tao
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.09108

Abstract

We present Lyapunov-type conditions for non-strong ergodicity of Markov processes. Some concrete models are discussed including diffusion processes on Riemannian manifolds and Ornstein-Uhlenbeck processes driven by symmetric α-stable processes. For SDE driven by α-stable process (α∈ (0,2]) with polynomial drift, the strong ergodicity or not is independent on α.

Related

• Subgeometric ergodicity of strong Markov processes
• Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state
• Ergodic properties of a class of non-Markovian processes
• Ergodic properties of generalized Ornstein--Uhlenbeck processes
• Exponential ergodicity of the solutions to SDE's with a jump noise