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Short Communications

On the first passage time of diffusion processes for time-dependent boundaries

V. A. Lebedev

Moscow

Abstract: In the paper, an inequality is obtained (see Theorem) which is closely connected with first passage problems for diffusion processes for a special class of boundaries.
Usefulness of the theorem is illustrated by two examples one of which is a short proof of a recent result due to L. A. Shepp [3].

Received: 20.05.1969

 English version: Theory of Probability and its Applications, 1971, 16:3, 541–545

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