A forward-backward stochastic algorithm for quasi-linear PDEs

• 成果类型: Article
• 署名作者: Delarue, F; Menozzi, S
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000674
• 发表日期: 2006
• 页码: 140-184
• 关键词: differential-equations; parabolic equations; approximation

摘要

We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully Coupled forward-backward SDEs, which provides an efficient probabilistic representation of this type of equation. The derivated algorithm holds for strong solutions defined oil any interval of arbitrary length. As a bypass product, We obtain a discretization procedure for the underlying FBSDE. In particular, our work provides an alternative to the method described in [Douglas, Ma and Protter (1996) Ann. Appl. Probab. 6 940-969] and weakens the regularity assumptions required in this reference.