The inverse first-passage problem for a Wiener process $(W_t)_{t \ge 0}$ seeks to determine a function $b:\mathbb{R}_+ \rightarrow \mathbb{R}$ such that $$\tau = \inf \>\{ \,t>0 \mid W_t \ge b(t) \,\}$$ 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 application are enlighted.

### On the Inverse First-Passage-Time Problem for a Wiener Process

#### Abstract

The inverse first-passage problem for a Wiener process $(W_t)_{t \ge 0}$ seeks to determine a function $b:\mathbb{R}_+ \rightarrow \mathbb{R}$ such that $$\tau = \inf \>\{ \,t>0 \mid W_t \ge b(t) \,\}$$ 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 application are enlighted.
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http://arxiv.org/pdf/0908.4213.pdf
Inverse first-passage problem; Wiener process; stopping time
Zucca C; Sacerdote L
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/55899