The Annals of Probability
- Ann. Probab.
- Volume 44, Number 1 (2016), 360-398.
On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces
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.
Ann. Probab., Volume 44, Number 1 (2016), 360-398.
Received: April 2013
Revised: September 2014
First available in Project Euclid: 2 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]
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