On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces
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Publication:272959
DOI10.1214/14-AOP976zbMATH Open1336.60125arXiv1304.5687OpenAlexW1547917734MaRDI QIDQ272959
Author name not available (Why is that?)
Publication date: 21 April 2016
Published in: (Search for Journal in Brave)
Abstract: This paper is concerned with solution in H"{o}lder 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 H"{o}lder spaces for them and give some inequalities among these H"{o}lder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.
Full work available at URL: https://arxiv.org/abs/1304.5687
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