The inverse first-passage problem for a Wiener process (Wt)t≥0 seeks to determine a function b: ℝ+→ℝ such that
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τ=inf{t>0|Wt≥b(t)}
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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.
Publié le : 2009-08-15
Classification:
Inverse first-passage problem,
Wiener process,
stopping time,
60K35,
60J65,
65C05,
65R20,
60G40,
45G10
@article{1248700619,
author = {Zucca, Cristina and Sacerdote, Laura},
title = {On the inverse first-passage-time problem for a Wiener process},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 1319-1346},
language = {en},
url = {http://dml.mathdoc.fr/item/1248700619}
}
Zucca, Cristina; Sacerdote, Laura. On the inverse first-passage-time problem for a Wiener process. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 1319-1346. http://gdmltest.u-ga.fr/item/1248700619/