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January 2016 On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces
Shanjian Tang, Wenning Wei
Ann. Probab. 44(1): 360-398 (January 2016). DOI: 10.1214/14-AOP976

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.

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Shanjian Tang. Wenning Wei. "On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces." Ann. Probab. 44 (1) 360 - 398, January 2016. https://doi.org/10.1214/14-AOP976

Information

Received: 1 April 2013; Revised: 1 September 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1336.60125
MathSciNet: MR3456341
Digital Object Identifier: 10.1214/14-AOP976

Subjects:
Primary: 60H15
Secondary: 35R60

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 1 • January 2016
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