An implicit numerical scheme for a class of backward doubly stochastic differential equations

Yaozhong Hu, David Nualart and Xiaoming Song

Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3295-3324

Abstract: In this paper, we consider a class of backward doubly stochastic differential equations (BDSDEs for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the techniques of Malliavin calculus, we are able to establish the Lp-Hölder continuity of the solution pair. Then, an implicit numerical scheme for the BDSDE is proposed and the rate of convergence is obtained in the Lp-sense. As a by-product, we obtain an explicit representation of the process Y in the solution pair to a linear BDSDE with random coefficients.

Keywords: Malliavin calculus; Backward doubly stochastic differential equations; Explicit solution to linear BDSDE; Implicit scheme; Hölder continuity of the solution pairs; Rate of convergence (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.09.014

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