1. Numerical Solutions of Stochastic Differential Delay Equations with Jumps.
- Author
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Jacob, Niels, Yongtian Wang, and Chenggui Yuan
- Subjects
- *
STOCHASTIC differential equations , *DIFFERENTIAL equations , *DELAY differential equations , *FUNCTIONAL differential equations , *LANGEVIN equations - Abstract
In this article, 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. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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