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Extension technique for functions of diffusion operators : a stochastic approach
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Assing, Sigurd and Herman, John (2021) Extension technique for functions of diffusion operators : a stochastic approach. Electronic Journal of Probability, 26 . pp. 1-32. doi:10.1214/21-EJP624 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/21-EJP624
Abstract
It has recently been shown that complete Bernstein functions of the Laplace operator map the Dirichlet boundary condition of a related elliptic PDE to the Neumann boundary condition. The importance of this mapping consists in being able to convert problems involving non-local operators, like fractional Laplacians, into ones that only involve differential operators. We generalise this result to diffusion operators associated with stochastic differential equations, using a method which is entirely based on stochastic analysis.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Dirichlet problem , Neumann problem , Differential equations, Elliptic, Stochastic differential equations | ||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||
Publisher: | Institute of Mathematical Statistics and Bernoulli Society | ||||||
ISSN: | 1083-6489 | ||||||
Official Date: | 12 May 2021 | ||||||
Dates: |
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Volume: | 26 | ||||||
Page Range: | pp. 1-32 | ||||||
DOI: | 10.1214/21-EJP624 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 20 July 2021 | ||||||
Date of first compliant Open Access: | 21 July 2021 | ||||||
RIOXX Funder/Project Grant: |
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