Abstract:
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.
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