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An approximation for the inverse first passage time problem

Part of: Partial differential equations, boundary value problems Markov processes Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  01 July 2016

Jing-Sheng Song  and
Paul Zipkin
Jing-Sheng Song*
Affiliation:
Duke University
Paul Zipkin*
Affiliation:
Duke University
*
∗ Postal address: Fuqua School of Business, Duke University, Durham, NC, USA.
∗ Postal address: Fuqua School of Business, Duke University, Durham, NC, USA.
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Abstract

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We propose an approximation for the inverse first passage time problem. It is similar in spirit and method to the tangent approximation for the original first passage time problem. We provide evidence that the technique is quite accurate in many cases. We also identify some cases where the approximation performs poorly.

Keywords

Inverse first passage timeWiener processapproximation

MSC classification

Primary: 60J65: Brownian motion
Secondary: 65N21: Inverse problems 58J35: Heat and other parabolic equation methods
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 1 , March 2011 , pp. 264 - 275
Copyright
Copyright © Applied Probability Trust 2011 

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