TY - JOUR
T1 - Strong Convergence of Jump-Adapted Implicit Milstein Method for a Class of Nonlinear Jump-Diffusion Problems
AU - Yang , Xu
AU - Zhao , Weidong
JO - Journal of Computational Mathematics
VL - 1
SP - 248
EP - 270
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2206-m2021-0354
UR - https://global-sci.org/intro/article_detail/jcm/22159.html
KW - Jump-diffusion, Jump-adapted implicit Milstein method, Poisson jumps, Strong
convergence rate, Non-Lipschitz coefficients.
AB - <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>