On the inverse first-passage-time problem for a Wiener process

Details On the inverse first-passage-time problem for a Wiener process On the inverse first-passage-time problem for a Wiener process

2009-08-28

arxiv.org/abs/0908.4213v1

Annals of Applied Probability 2009, Vol. 19, No. 4, 1319-1346

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP571 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP571

The inverse first-passage problem for a Wiener process $(W_t)_{t\ge0}$ seeks to determine a function $b{}:{}\mathbb{R}_+\to\mathbb{R}$ such that \[\tau=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In this paper two methods for approximating the unknown function $b$ are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.

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