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Zbl 1168.60356
Jacob, Niels; Wang, Yongtian; Yuan, Chenggui
Numerical solutions of stochastic differential delay equations with jumps. (English)
[J] Stochastic Anal. Appl. 27, No. 4, 825-853 (2009). ISSN 0736-2994; ISSN 1532-9356/e

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 $\log R$.

MSC 2000:: *60H35 Computational methods for stochastic equations
60H10 Stochastic ordinary differential equations
34K20 Stability theory of functional-differential equations
34K50 Stochastic delay equations

Keywords: convergence rate; Euler-Maruyama method; stochastic differential delay equations; stochastic theta method

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Zentralblatt MATH Berlin [Germany]