STRONG CONVERGENCE OF JUMP-ADAPTED IMPLICIT MILSTEIN METHOD FOR A CLASS OF NONLINEAR JUMP-DIFFUSION PROBLEMS  

作　　者：Xu Yang Weidong Zhao 

机构地区：[1]School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China [2]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Journal of Computational Mathematics》2024年第1期248-270,共23页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11901565,12071261,11831010,11871068);by the Science Challenge Project(No.TZ2018001);by National Key R&D Plan of China(Grant No.2018YFA0703900).

摘　　要：In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.

关 键 词：JUMP-DIFFUSION Jump-adapted implicit Milstein method Poisson jumps Strong convergence rate Non-Lipschitz coefficients 

分 类 号：O17[理学—数学]