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On the inverse first-passage-time problem for a Wiener process. (English) Zbl 1173.60344

Summary: The inverse first-passage problem for a Wiener process \((W_t)_{t\geq 0}\) seeks to determine a function \(b: \mathbb R_{+}\rightarrow \mathbb R\) such that \[ \tau =\inf{t>0|W_t\geq b(t)} \] 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J65 Brownian motion
65C05 Monte Carlo methods
65R20 Numerical methods for integral equations
60G40 Stopping times; optimal stopping problems; gambling theory
45G10 Other nonlinear integral equations
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