Strong Convergence of Jump-Adapted Implicit Milstein Method for a Class of Nonlinear Jump-Diffusion Problems
Year: 2024
Author: Xu Yang, Weidong Zhao
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 248–270
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2206-m2021-0354
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 248–270
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Jump-diffusion Jump-adapted implicit Milstein method Poisson jumps Strong convergence rate Non-Lipschitz coefficients.