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An elementary approach to the inverse first-passage-time problem for soft-killed Brownian motion

Part of: Distribution theory - Probability Stochastic processes Markov processes

Published online by Cambridge University Press:  04 July 2023

Alexander Klump  and
Martin Kolb
Alexander Klump*
Affiliation:
Paderborn University
Martin Kolb*
Affiliation:
Paderborn University
*
*Postal address: Institute of Mathematics, Paderborn University, Germany, 33098 Paderborn, Warburger Straße 100.
*Postal address: Institute of Mathematics, Paderborn University, Germany, 33098 Paderborn, Warburger Straße 100.
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Abstract

We prove existence and uniqueness for the inverse-first-passage time problem for soft-killed Brownian motion using rather elementary methods relying on basic results from probability theory only. We completely avoid the relation to a suitable partial differential equation via a suitable Feynman–Kac representation, which was previously one of the main tools.

Keywords

Inverse first-passage-time problemboundary crossingBrownian motiondiffusionsoft killingstochastic ordering

MSC classification

Primary: 60J65: Brownian motion
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 1 , March 2024 , pp. 279 - 300
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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