The Annals of Probability

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

Shanjian Tang and Wenning Wei

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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.

Article information

Source
Ann. Probab., Volume 44, Number 1 (2016), 360-398.

Dates
Received: April 2013
Revised: September 2014
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1454423044

Digital Object Identifier
doi:10.1214/14-AOP976

Mathematical Reviews number (MathSciNet)
MR3456341

Zentralblatt MATH identifier
1336.60125

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Keywords
Backward stochastic partial differential equations backward stochastic differential equations Hölder space heat potential

Citation

Tang, Shanjian; Wei, Wenning. On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces. Ann. Probab. 44 (2016), no. 1, 360--398. doi:10.1214/14-AOP976. https://projecteuclid.org/euclid.aop/1454423044


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