@Article{JCM-42-1,
author = {Yang, Xu and Zhao, Weidong},
title = {Strong Convergence of Jump-Adapted Implicit Milstein Method for a Class of Nonlinear Jump-Diffusion Problems},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {1},
pages = {248--270},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2206-m2021-0354},
url = {https://global-sci.com/article/84084/strong-convergence-of-jump-adapted-implicit-milstein-method-for-a-class-of-nonlinear-jump-diffusion-problems}
}