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Teoriya Veroyatnostei i ee Primeneniya, 1965, Volume 10, Issue 2, Pages 360–364
(Mi tvp530)
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This article is cited in 32 scientific papers (total in 32 papers)
Short Communications
О времени первого прохождения для одного класса процессов с независимыми приращениями
A. A. Borovkov Institute of Mathematics, Siberian Branch of USSR Academy of Sciences
Abstract:
In the paper we generalize an observation of Keilson [1]. Let $X(t)$ be a left continuous homogeneous stochastic process with independent increments and let us suppose that its trajectories are continuous from above ($X(t+0)-X(t)\le0$) with probability 1. For such processes the indentity
$$
h(x,t)=\frac xtf(x,t)
$$
is obtained where $f(x,t)$ and $h(x,t)$ are generalized densities for $X(t)$ and for the first passage time of the level $x>0$ respectively.
Received: 08.07.1964
Citation:
A. A. Borovkov, “О времени первого прохождения для одного класса процессов с независимыми приращениями”, Teor. Veroyatnost. i Primenen., 10:2 (1965), 360–364; Theory Probab. Appl., 10:2 (1965), 331–334
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