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

Reinhard Hoepfner; Eva Loecherbach

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

Probability 2011-03-09 v3

Authors: Reinhard Hoepfner , Eva Loecherbach

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.

Keywords

time inhomogeneous Markov process T-periodic semigroup ergodicity grid chain degenerate diffusion

Cite

@article{arxiv.1012.4916,
  title  = {On some ergodicity properties for time inhomogeneous Markov processes with $T$-periodic semigroup},
  author = {Reinhard Hoepfner and Eva Loecherbach},
  journal= {arXiv preprint arXiv:1012.4916},
  year   = {2011}
}

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