RUS  ENG
Full version
JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1965 Volume 10, Issue 2, Pages 360–364 (Mi tvp530)

This article is cited 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


 English version:
Theory of Probability and its Applications, 1965, 10:2, 331–334

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024