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Stochastic and partial differential equations on non-smooth time-dependent domains
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Department of Mathematics, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden.
2019 (engelsk)Inngår i: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 129, nr 4, s. 1097-1131Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this article, we consider non-smooth time-dependent domains whose boundary is W1,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.

sted, utgiver, år, opplag, sider
Elsevier, 2019. Vol. 129, nr 4, s. 1097-1131
Emneord [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
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Identifikatorer
URN: urn:nbn:se:umu:diva-152844DOI: 10.1016/j.spa.2018.04.006ISI: 000462111300001Scopus ID: 2-s2.0-85047257163OAI: oai:DiVA.org:umu-152844DiVA, id: diva2:1259083
Tilgjengelig fra: 2018-10-27 Laget: 2018-10-27 Sist oppdatert: 2019-10-11bibliografisk kontrollert

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