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

摘要

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.