Markov intervention of chance, and limit theorems

V. M. Shurenkov

Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 161-183

Résumé

This article concerns properties of random processes $\mathfrak z_t$ ($t\geqslant0$) for which a Markov intervention time exists, i.e., a nonnegative random variable $\mathfrak w$ such that for a particular value of $\mathfrak z_{\mathfrak w}$ the collections $\{\mathfrak z_t\ (0\leqslant t\mathfrak w)\}$ and $\{\mathfrak z_{t+\mathfrak w}\ (t\geqslant0)\}$ are conditionally independent, and the conditional distributions of $\{\mathfrak z_{t+\mathfrak w}\ (t\geqslant0)\}$ (under the condition $\mathfrak z_{\mathfrak w}=x$) and $\{\mathfrak z_t\ (t\geqslant0)\}$ (under the condition $\mathfrak z_0=x$) coincide. Such random processes generalize Markov and semi-Markov processes. Bibliography: 10 titles.