On forward and backward SPDEs with non-local boundary conditions

We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the solution at different times, including the termi...

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Main Author: Dokuchaev, Nikolai
Format: Journal Article
Published: American Institute of Mathematical Sciences 2015
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/34666
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author Dokuchaev, Nikolai
author_facet Dokuchaev, Nikolai
author_sort Dokuchaev, Nikolai
building Curtin Institutional Repository
collection Online Access
description We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the solution at different times, including the terminal time, initial time and continuously distributed times. For the case of backward equations, this setting covers almost surely periodicity. Uniqueness, solvability and regularity results for the solutions are obtained. Some possible applications to portfolio selection are discussed.
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spelling curtin-20.500.11937-346662017-09-13T15:56:20Z On forward and backward SPDEs with non-local boundary conditions Dokuchaev, Nikolai backward SPDEs portfolio selection periodic conditions non-local conditions SPDEs We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the solution at different times, including the terminal time, initial time and continuously distributed times. For the case of backward equations, this setting covers almost surely periodicity. Uniqueness, solvability and regularity results for the solutions are obtained. Some possible applications to portfolio selection are discussed. 2015 Journal Article http://hdl.handle.net/20.500.11937/34666 10.3934/dcds.2015.35.5335 American Institute of Mathematical Sciences fulltext
spellingShingle backward SPDEs
portfolio selection
periodic conditions
non-local conditions
SPDEs
Dokuchaev, Nikolai
On forward and backward SPDEs with non-local boundary conditions
title On forward and backward SPDEs with non-local boundary conditions
title_full On forward and backward SPDEs with non-local boundary conditions
title_fullStr On forward and backward SPDEs with non-local boundary conditions
title_full_unstemmed On forward and backward SPDEs with non-local boundary conditions
title_short On forward and backward SPDEs with non-local boundary conditions
title_sort on forward and backward spdes with non-local boundary conditions
topic backward SPDEs
portfolio selection
periodic conditions
non-local conditions
SPDEs
url http://hdl.handle.net/20.500.11937/34666