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Numerical solutions of stochastic differential delay equations with jumps. (English) Zbl 1168.60356
Summary: We investigate the strong convergence of the Euler-Maruyama method and stochastic theta method for stochastic differential delay equations with jumps. Under a global Lipschitz condition, we not only prove the strong convergence, but also obtain the rate of convergence. We show strong convergence under a local Lipschitz condition and a linear growth condition. Moreover, it is the first time that we obtain the rate of the strong convergence under a local Lipschitz condition and a linear growth condition, i.e., if the local Lipschitz constants for balls of radius $R$ are supposed to grow not faster than $logR$.
MSC:
 60H35 Computational methods for stochastic equations 60H10 Stochastic ordinary differential equations 34K20 Stability theory of functional-differential equations 34K50 Stochastic functional-differential equations