On forward and backward SPDEs with non-local boundary conditions

Nikolai Dokuchaev

doi:10.3934/dcds.2015.35.5335

Article Contents

2015, Volume 35, Issue 11: 5335-5351. Doi: 10.3934/dcds.2015.35.5335

This issue Previous Article Degenerate backward SPDEs in bounded domains and applications to barrier options Next Article On the Cauchy-Dirichlet problem in a half space for backward SPDEs in weighted Hölder spaces

On forward and backward SPDEs with non-local boundary conditions

Nikolai Dokuchaev^1,

1.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, Western Australia, 6845

Received: October 31, 2012

Revised: March 31, 2014

Published: October 2015

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Abstract

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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Mathematics Subject Classification: Primary: 60J55, 60J60, 60H10; Secondary: 34F05, 34G10.

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