Electronic Communications in Probability

Representation theorems for SPDEs via backward doubly

Auguste Aman, Abouo Elouaflin, and Mamadou Diop

Full-text: Open access

Abstract

In this paper we establish a probabilistic representation for the spatial gradient ofthe viscosity solution to a quasilinear parabolic stochastic partial differential equations(SPDE, for short) in the spirit of the Feynman-Kac formula, without using thederivatives of the coefficients of the corresponding backward doubly stochastic differentialequations (FBDSDE, for short).

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 64, 15 pp.

Dates
Accepted: 25 July 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315603

Digital Object Identifier
doi:10.1214/ECP.v18-2223

Mathematical Reviews number (MathSciNet)
MR3084575

Zentralblatt MATH identifier
1329.60206

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60H20: Stochastic integral equations 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Backward doubly SDEs stochastic partial differential equation stochastic viscosity

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Aman, Auguste; Elouaflin, Abouo; Diop, Mamadou. Representation theorems for SPDEs via backward doubly. Electron. Commun. Probab. 18 (2013), paper no. 64, 15 pp. doi:10.1214/ECP.v18-2223. https://projecteuclid.org/euclid.ecp/1465315603


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