A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels

QIAN Siying; ZHANG Jingna; HUANG Jianfei

doi:10.21656/1000-0887.420067

Volume 42 Issue 11

Nov. 2021

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QIAN Siying, ZHANG Jingna, HUANG Jianfei. A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1203-1212. doi: 10.21656/1000-0887.420067

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A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels

doi: 10.21656/1000-0887.420067

A Modified EulerMaruyama Scheme for MultiTerm Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels

Funds:

The National Natural Science Foundation of China(11701502；11871065)

Received Date: 2021-03-15
Rev Recd Date: 2021-04-26

Available Online: 2021-12-07

Abstract

Abstract

A modified Euler-Maruyama (EM) scheme was constructed for a class of multi-term fractional nonlinear stochastic differential equations with weak singularity kernels, and the strong convergence of this modified EM scheme was proved. Specifically, according to the sufficient condition for stochastic integral decomposition, the multi-term fractional stochastic differential equation was equivalently transformed into the stochastic Volterra integral equation, and then the corresponding modified EM scheme and its strong convergence were derived and proved, respectively. The order of strong convergence is α_m-α_m-1, where α_i is the index of fractional derivative satisfying 0<α₁<…<α_m-1<α_m<1. Finally, numerical experiments verify the correctness of the theoretical results.
- multi-term fractional stochastic differential equation,
- weakly singular kernel,
- Euler-Maruyama scheme,
- strong convergence

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References(19)

References

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