The paper deals with strong global approximation of SDEs driven by twoindependent processes: a nonhomogeneous Poisson process and a Wiener process.We assume that the jump and diffusion coefficients of the underlying SDEsatisfy jump commutativity condition. We establish the exact convergence rateof minimal errors that can be achieved by arbitrary algorithms based on afinite number of observations of the Poisson and Wiener processes. We considerclasses of methods that use equidistant or nonequidistant sampling of thePoisson and Wiener processes. We provide a construction of optimal methods,based on the classical Milstein scheme, which asymptotically attain theestablished minimal errors. The analysis implies that methods based onnonequidistant mesh are more efficient than those based on the equidistantmesh.
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