Weak approximation of stochastic differential equations with jumps

We develop adaptive time stepping methods, based on the Monte Carlo Euler method, for weak approximation of jump diffusion driven stochastic differential equations. The main result is new expansions of the computational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual back-ward problems. The expansions lead to efficient and accurate computation of error estimates. We describe adaptive algorithms for either stochastic time steps or quasi-deterministic time steps and present numerical examples illustrating their behavior.