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Short Communications

On Convergence of Sums of Step Stochastic Processes to a Poisson Process

B. Grigelionis

Vilnius

Abstract: Let $X_n (t)=\sum_{r-1}^{k_n}X_{nr}(t)$, where $X_{nr}(t)$ are independent asymptotically negligible stochastic processes with non-negative integer-valued increments. The necessary and sufficient conditions for convergence of the sequence $\{X_n(t)\}$ to a given Poisson process are proved.

Received: 14.09.1961

 English version: Theory of Probability and its Applications, 1963, 8:2, 177–182