Optimal global approximation of jump-diffusion SDEs via path-independent step-size control

We provide a construction of an implementable method based on path-independent adaptive step-size control for global approximation of jump-diffusion SDEs. The sampling points are chosen in nonadaptive way with respect to trajectories of the driving Poisson and Wiener processes. However, they are adapted to the diffusion and jump coefficients of the underlying stochastic differential equation and to the values of intensity function of the driving Poisson process. The method is asymptotically optimal in the class of methods that use (possibly) non-equidistant discretization of the interval [0,T] and is more efficient than any method based on the uniform mesh.