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Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise
This paper proposes a general symplectic Euler scheme for a class of Ham...
06/28/2020 ∙ by Qingyi Zhan, et al. ∙
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The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations
This paper focuses on explicit approximations for nonlinear stochastic d...
08/19/2020 ∙ by Guoting Song, et al. ∙
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Strong convergence rate of the truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps
In this paper, we study a class of super-linear stochastic differential ...
09/07/2020 ∙ by Shuaibin Gao, et al. ∙
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Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations
In this article we introduce several kinds of easily implementable expli...
02/17/2020 ∙ by Xiaoyue Li, et al. ∙
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On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes
We introduce and study a notion of Asymptotic Preserving schemes, relate...
11/04/2020 ∙ by Charles-Edouard Bréhier, et al. ∙
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Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flows
In this paper, we propose stochastic structure-preserving schemes to com...
06/21/2019 ∙ by Junlong Lyu, et al. ∙
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Numerical Methods for Backward Stochastic Differential Equations: A Survey
Backwards Stochastic Differential Equations (BSDEs) have been widely emp...
01/22/2021 ∙ by Jared Chessari, et al. ∙
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Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations
10/30/2020 ∙ by Yulian Yi, et al. ∙
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In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the numerical solutions are positive. Under some reasonable conditions, we obtain the convergence and the convergence rate results for these methods. The main difficulty is to obtain the strong convergence and the convergence rate for stochastic differential equations whose coefficients are of exponential growth. Some numerical experiments are provided to illustrate the theoretical results for our schemes.
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