Strong Convergence of Jump-Adapted Implicit Milstein Method for a Class of Nonlinear Jump-Diffusion Problems (Journal of Computational Mathematics, 2023)
In this paper, we study the strong convergence of a jump-adapted implicit Milsteinmethod for a class of jump-diffusion stochastic differential equations with non-globallyLipschitz drift coefficients. Compared with the regular methods, the jump-adapted methods can significantly reduce the complexity of higher order methods, which makes themeasily implementable for scenario simulation. However, due to the fact that jump-adaptedtime 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-globallyLipschitz setting. We provide a rigorous strong convergence analysis of the consideredjump-adapted implicit Milstein method by developing some novel analysis techniques andoptimal rate with order one is also successfully recovered. Numerical experiments arecarried out to verify the theoretical findings.