This article is cited in 9 papers

Remarks about the limit of composite random function

D. S. Sil'vestrov

Kiev

Abstract: Let $\xi_{\varepsilon}(t)$, $t\geq 0$, be a continuous from the right stochastic process without discontinuities of the second kind and $\nu_{\varepsilon}$, for each $\varepsilon\geq 0$, be a non-negative random variable.
In the paper, general sufficient conditions are studied for weak convergence of the distribution functions of the random variables $\xi_{\varepsilon}(\nu_{\varepsilon})$ to the distribution function of $\varepsilon_0(\nu_0)$ as $\varepsilon\to 0$.

Received: 14.01.1971

 English version: Theory of Probability and its Applications, 1973, 17:4, 669–677

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