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Short Communications

Analytical Properties of a Generating Function for a Number of Renewals

Yu. K. Belyaev, V. M. Maksimov

Moscow

Abstract: Let $\{t_i\}$ be a renewal process, $N_t=\max(n:t_n<t)$. Some analytic properties, such as analyticy within the circle $|z|<{1/r}$, of the function $\Pi _t (z)=\sum _{k=0}^\infty z^k P\{N_t=k\}$ and others are proved.

Received: 03.11.1961

 English version: Theory of Probability and its Applications, 1963, 8:1, 102–105