A first order semi-discrete algorithm for backward doubly stochastic differential equations

Feng Bao; Yanzhao Cao; Weidong Zhao

doi:10.3934/dcdsb.2015.20.1297

Article Contents

2015, Volume 20, Issue 5: 1297-1313. Doi: 10.3934/dcdsb.2015.20.1297

This issue Previous Article Special section on differential equations: Theory, application, and numerical approximation Next Article Stability and convergence of time-stepping methods for a nonlocal model for diffusion

A first order semi-discrete algorithm for backward doubly stochastic differential equations

1.
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849
2.
Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849
3.
School of Mathematics, Shandong University, Jinan, Shandong

Received: June 30, 2013

Revised: December 31, 2014

Published: June 2015

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Abstract

Numerical solutions of backward doubly stochastic differential equations (BDSDES) and the related stochastic partial differential equations (Zakai equations) are considered. First order algorithms are constructed using a generalized Itô-Taylor formula for two-sided stochastic differentials. The convergence order is proved through rigorous error analysis. Numerical experiments are carried out to verify the theoretical results and to demonstrate the efficiency of the proposed numerical algorithms.

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Mathematics Subject Classification: Primary: 52B10, 65D18, 68U05; Secondary: 68U07.

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