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Strong approximations of stochastic differential equations with jumps. (English) Zbl 1121.65007

Methods yielding strong approximations of stochastic differential equations (SDEs) driven by Wiener processes and Poisson random measures are surveyed. Next, significantly less complicated discrete time approximation schemes are devised for pure jump SDEs. For these equations, strong order of convergence of higher-order Taylor schemes is proved under less restrictive hypotheses than required for more general SDEs.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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