On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces

Abstract

This paper is concerned with solution in Hölder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic spatial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional Hölder spaces for them and give some inequalities among these Hölder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.

Published at http://dx.doi.org/10.1214/14-AOP976 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• On the Dirichlet Problem for Backward Parabolic Stochastic Partial Differential Equations in General Smooth Domains

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• Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition
• Stochastic Path-Dependent Hamilton-Jacobi-Bellman Equations and Controlled Stochastic Differential Equations with Random Path-Dependent Coefficients