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The moving-eigenvalue method: hitting time for Itô processes and moving boundaries
RISE Research Institutes of Sweden, Digital Systems, Data Science.ORCID iD: 0000-0002-7504-0328
2020 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 53, no 40, article id 405201Article in journal (Refereed) Published
Abstract [en]

We present simple solutions of first-passage and first-exit time problems for general moving boundaries and general Itô processes in one dimension, including diffusion processes with convection. The approach uses eigenfunction expansion, despite the boundary time-variability that, until now, has been an obstacle for spectral methods. The eigenfunction expansion enables the analytical reduction of the problem to a set of equivalent ordinary differential equations, which can be input directly to readily available solvers. The method is thus suitable as a basis for efficient numerical computation. We illustrate the technique by application to Wiener and Ornstein–Uhlenbeck processes for a variety of moving boundaries, including cases for which exact results are known.

Place, publisher, year, edition, pages
IOP Publishing , 2020. Vol. 53, no 40, article id 405201
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Natural Sciences
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URN: urn:nbn:se:ri:diva-48274DOI: 10.1088/1751-8121/ab9c59Scopus ID: 2-s2.0-85092335189OAI: oai:DiVA.org:ri-48274DiVA, id: diva2:1464428
Available from: 2020-09-07 Created: 2020-09-07 Last updated: 2023-05-25Bibliographically approved

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Nilsson, Martin

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