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Stochastic and partial differential equations on non-smooth time-dependent domains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0003-2716-3195
2019 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 129, no 4, p. 1097-1131Article in journal (Refereed) Published
Abstract [en]

In this article, we consider non-smooth time-dependent domains whose boundary is W^{1,p} in time and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron’s method, we also conclude existence of viscosity solutions. Our results generalize two articles by Dupuis and Ishii to time-dependent domains.

Place, publisher, year, edition, pages
2019. Vol. 129, no 4, p. 1097-1131
Keywords [en]
Reflected diffusion; Skorohod problem; Oblique reflection; Time-dependent domain; Stochastic differential equations; Non-smooth domain; Viscosity solution; Parabolic partial differential equation; Comparison principle; Existence; Uniqueness
National Category
Probability Theory and Statistics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249062DOI: 10.1016/j.spa.2018.04.006ISI: 000462111300001Scopus ID: 2-s2.0-85047257163OAI: oai:DiVA.org:kth-249062DiVA, id: diva2:1303762
Note

QC 20190502

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-08-27Bibliographically approved

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Önskog, Thomas

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