The Annals of Applied Probability

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

Cristina Zucca and Laura Sacerdote

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Abstract

The inverse first-passage problem for a Wiener process (Wt)t≥0 seeks to determine a function b: ℝ+→ℝ such that

τ=inf{t>0|Wtb(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.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 4 (2009), 1319-1346.

Dates
First available in Project Euclid: 27 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1248700619

Digital Object Identifier
doi:10.1214/08-AAP571

Mathematical Reviews number (MathSciNet)
MR2538072

Zentralblatt MATH identifier
1173.60344

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J65: Brownian motion [See also 58J65] 65C05: Monte Carlo methods 65R20: Integral equations
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 45G10: Other nonlinear integral equations

Keywords
Inverse first-passage problem Wiener process stopping time

Citation

Zucca, Cristina; Sacerdote, Laura. On the inverse first-passage-time problem for a Wiener process. Ann. Appl. Probab. 19 (2009), no. 4, 1319--1346. doi:10.1214/08-AAP571. https://projecteuclid.org/euclid.aoap/1248700619


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