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In this rather demanding chapter we present the Wagner-Platen expansion for solutions of SDEs with jumps. This stochastic expansion generalizes the deterministic Taylor formula and the Wagner-Platen expansion for diffusions to the case of SDEs with jumps. It allows expanding the increments of smooth functions of Itô processes in terms of multiple stochastic integrals. As we will see, it is the key tool for the construction of stochastic numerical methods and very convenient for other approximation tasks.
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