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First Passage Problems for Asymmetric Wiener Processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Mario Lefebvre
Mario Lefebvre*
Affiliation:
École Polytechnique de Montréal
*
∗ Postal address: Département de Mathématiques et de Génie Industriel, École Polytechnique, C.P. 6079, Succursale Centre-ville, Montréal, Québec, Canada H3C 3A7. Email address: mario.lefebvre@polymtl.ca
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Abstract

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The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

Keywords

Hitting timeBrownian motionKolmogorov equation

MSC classification

Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 175 - 184
Copyright
© Applied Probability Trust 2006 

References

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