On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces. (English) Zbl 1336.60125
Summary: This paper is concerned with the 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 for deterministic PDEs.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
Keywords:
backward stochastic partial differential equations; Cauchy problem; Hölder spaces; heat potentialReferences:
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