This article is cited in 3 papers

Short Communications

An ergodic theorem for regenerating processes

G. P. Klimov

Moscow

Abstract: Let $\xi(t)$, $t\ge 0$, be a regenerating process; $B$ be a measurable set in the phase space; $x(t)$ be the indicator of the event $\{\xi(t)\in B\}$.
In this paper, a theorem is proved on convergence of $\displaystyle\frac{1}{T}\int_0^T x(t)\,dt$ to a final probability of the event $\{\xi(t)\in B\}$ as $T\to\infty$.

Received: 27.12.1974

 English version: Theory of Probability and its Applications, 1977, 21:2, 392–395

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