Numerical Solutions of Stochastic Differential Delay Equations with Jumps |
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Authors: | Niels Jacob Yongtian Wang |
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Affiliation: | Department of Mathematics , Swansea University , Swansea , United Kingdom |
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Abstract: | 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. |
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Keywords: | Convergence rate Euler–Maruyama method Stochastic differential delay equations Stochastic theta method |
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