hal-00196841, version 2
Representation Theorems for Backward Doubly Stochastic Differential Equations
Preprint of Laboratoire de Mathematiques Appliquée et informatique (2008)
Abstract: In this paper we study the class of backward doubly stochastic differential equations (BDSDEs, for short) whose terminal value depends on the history of forward diffusion. We first establish a probabilistic representation for the spatial gradient of the stochastic viscosity solution to a quasilinear parabolic SPDE in the spirit of the Feynman-Kac formula, without using the derivatives of the coefficients of the corresponding BDSDE. Then such a representation leads to a closed-form representation of the martingale integrand of BDSDE, under only standard Lipschitz condition on the coefficients.
- 1:
- Université de Cocody
- Domain : Mathematics/Probability
- Keywords : Backward doubly SDEs – Stochastic Partial Differential equation – Adapted solution – anticipating stochastic calculus – stochastic viscosity solutions.
- Comment : This article will be submitt later
- Available versions : v1 (2007-12-13) v2 (2008-11-03) v3 (2008-11-07) v4 (2008-11-12)
- hal-00196841, version 2
- http://hal.archives-ouvertes.fr/hal-00196841
- oai:hal.archives-ouvertes.fr:hal-00196841
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- Submitted on: Monday, 3 November 2008 17:07:00
- Updated on: Monday, 3 November 2008 22:20:51
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