GENERAL FULL IMPLICIT STRONG TAYLOR APPROXIMATIONS FOR STIFF STOCHASTIC DIFFERENTIAL EQUATIONS  

作　　者：Kai Liu Guiding Gu 

机构地区：[1]School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China [2]College of Science,Hunan University of Technology and Business,Changsha 410205,China

出　　处：《Journal of Computational Mathematics》2022年第4期541-569,共29页计算数学（英文）

基　　金：supported by the Fundamental Research Funds for the Central Universities of China,and the second author is supported by the National Natural Fund Projects of China(Nos.11771100,12071332).

摘　　要：In this paper,we present the backward stochastic Taylor expansions for a Ito process,including backward Ito-Taylor expansions and backward Stratonovich-Taylor expansions.We construct the general full implicit strong Taylor approximations(including Ito-Taylor and Stratonovich-Taylor schemes)with implicitness in both the deterministic and the stochastic terms for the stiff stochastic differential equations(SSDE)by employing truncations of backward stochastic Taylor expansions.We demonstrate that these schemes will converge strongly with corresponding order 1,2,3,....Mean-square stability has been investigated for full implicit strong Stratonovich-Taylor scheme with order 2,and it has larger meansquare stability region than the explicit and the semi-implicit strong Stratonovich-Taylor schemes with order 2.We can improve the stability of simulations considerably without too much additional computational effort by using our full implicit schemes.The full implicit strong Taylor schemes allow a larger range of time step sizes than other schemes and are suitable for SSDE with stiffness on both the drift and the diffusion terms.Our numerical experiment show these points.

关 键 词：Stiff stochastic differential equations APPROXIMATIONS Backward Stochastic Taylor expansions Full implicit Taylor methods 

分 类 号：O24[理学—计算数学]