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On the moments of some first-passage times

Published online by Cambridge University Press:  14 July 2016

Valeri T. Stefanov
Valeri T. Stefanov*
Affiliation:
Institute of Mathematics, Sofia
*
∗ Postal address: Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373 1090-Sofia, Bulgaria.
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Abstract

Let {Xt }t≧0 (t may be discrete or continuous) be a random process whose finite-dimensional distributions are of exponential type. The first-passage time inf{t:Xt ≧f(t)}, where f(t) is a positive, continuous function, such that f(t)= o(t) as t↑∞, is considered. The problem of finiteness of its moments is solved for both the case that {Xt }t≧0 has stationary independent increments as well as the case in which no assumptions are made about stationarity and independence for the increments of the process. Applications to sequential estimation are also given.

Keywords

SEQUENTIAL ESTIMATION

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 461 - 466
Copyright
Copyright © Applied Probability Trust 1985 

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