Stationary distribution of Markov chains in \(\mathbb{R}^d\) with application to global random optimization (Q1380400)

For a Markov chain taking values in a bounded measurable subset of \(\mathbb{R}^d\) the analogs of standard notions of irreducibility and periodicity are defined. For irreducible and aperiodic chains satisfying certain regularity conditions the existence of stationary and long-run distributions is proved. As an example, the chains arising in the random global optimization are considered. Unfortunately, the connection of presented results with the general theory of Markov chains is not discussed.