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arXiv · 0908.4213

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

Cristina Zucca·Laura Sacerdote
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Abstract

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 \[τ=\inf\{t>0| W_t\ge b(t)\}\] 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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Cristina Zucca, Laura Sacerdote. 2009-08-28. On the inverse first-passage-time problem for a Wiener process. https://doi.org/10.1214/08-aap571

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