On the Cauchy problem for backward stochastic partial differential equations in H\"{o}lder spaces
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.
Keywords
Cite
@article{arxiv.1304.5687,
title = {On the Cauchy problem for backward stochastic partial differential equations in H\"{o}lder spaces},
author = {Shanjian Tang and Wenning Wei},
journal= {arXiv preprint arXiv:1304.5687},
year = {2016}
}
Comments
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)