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International Journal for Uncertainty Quantification

Impact factor: 0.967

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2011003508
pages 351-367

NUMERICAL SOLUTIONS FOR FORWARD BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS AND ZAKAI EQUATIONS

Feng Bao
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849
Yanzhao Cao
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849; School of Mathematics, Sun Yat Sun University, China
Weidong Zhao
School of Mathematics, Shangdong University, Jinan, China

ABSTRACT

The numerical solutions of decoupled forward backward doubly stochastic differential equations and the related stochastic partial differential equations (Zakai equations) are considered. Numerical algorithms are constructed using reference equations. Rate of convergence is obtained through rigorous error analysis. Numerical experiments are carried out to verify the rate of convergence results and to demonstrate the efficiency of the proposed numerical algorithms.