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The inverse first-passage problem and optimal stopping
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 26, no 5, 3154-3177 p.Article in journal (Refereed) Published
Abstract [en]

Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that the solution of the inverse first-passage problem coincides with the solution of a related optimal stopping problem. Consequently, methods from optimal stopping theory may be applied in the study of the inverse first passage problem. We illustrate this with a study of the associated integral equation for the boundary.

Place, publisher, year, edition, pages
2016. Vol. 26, no 5, 3154-3177 p.
Keyword [en]
Inverse first-passage problem, optimal stopping, nonlinear integral equation
National Category
Mathematics Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-283524DOI: 10.1214/16-AAP1172ISI: 000386864600017OAI: oai:DiVA.org:uu-283524DiVA: diva2:919260
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Available from: 2016-04-13 Created: 2016-04-13 Last updated: 2017-11-30Bibliographically approved

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Ekström, ErikJanson, Svante

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