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Stochastic barriers for the Wiener process

Published online by Cambridge University Press:  14 July 2016

C. Park  and
J. A. Beekman
C. Park*
Affiliation:
Miami University
J. A. Beekman*
Affiliation:
Ball State University
*
∗ Postal address: Department of Mathematics and Statistics, Bachelor Hall, Miami University, Oxford, OH 45056, U.S.A.
∗∗ Postal address: Department of Mathematical Sciences, Ball State University, Muncie IN 47306, U.S.A.
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Abstract

Let {W(t), 0 ≦ t < ∞} be the standard Wiener process. The probabilities of the type P[sup0≦t ≦ TW(t) − f(t) ≧ 0] have been extensively studied when f(t) is a deterministic function. This paper discusses the probabilities of the type P{sup0≦t ≦ TW(t) − [f(t) + X(t)] ≧ 0} when X(t) is a stochastic process. By taking compound Poisson processes as X(t), the paper gives procedures for finding such probabilities.

Keywords

STANDARD WIENER PROCESSSTOCHASTIC BARRIERDETERMINISTIC FUNCTIONSTATIONARY INDEPENDENT INCREMENTSSECTIONALLY CONTINUOUSNORMAL DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 338 - 348
Copyright
Copyright © Applied Probability Trust 1983 

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