On some ergodicity properties for time inhomogeneous Markov processes with $T$-periodic semigroup

Abstract

We consider a time inhomogeneous strong Markov process $({\xi }_t{)}_{t\ge 0}$ taking values in a Polish state space whose semigroup has a $T$-periodic structure. We give simple conditions which imply ergodicity of the grid chain $({\xi }_{kT}{)}_{k\in {\mathbb{N}}_0}$ In case of $d$-dimensional possibly degenerate diffusions, the conditions are stated in terms of drift and diffusion coefficient of the process.

References in corpus (1)

• The exit problem for diffusions with time-periodic drift and stochastic resonance

Cited by in corpus (2)

• On frequency estimation of periodic ergodic diffusion process
• Transition densities for stochastic Hodgkin-Huxley models