This article is cited in 9 papers

Short Communications

On moments of the time and the value of the first jump over a curvilinear bound

V. I. Rotar'

Moscow

Abstract: The maximal order of finite moments of the time and the value of the first jump over curvilinear bounds is obtained for the ordinary random walk with infinite variance. The negative answer is given to the question of professor H. Robbins about finiteness of the mean value of the positive part of the particle's position at a Markovian stopping time.

Received: 23.11.1966

 English version: Theory of Probability and its Applications, 1967, 12:4, 690–695

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