Backward Euler method for stochastic differential equations with non-Lipschitz coefficients

2022/05/26 by Zhou, Hao, Hu, Yaozhong, Liu, Yanghui · 3 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2205.13659

Abstract

We study the traditional backward Euler method for m-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter H > 1/2 whose drift coefficient satisfies the one-sided Lipschitz condition. The backward Euler scheme is proved to be of order 1 and this rate is optimal by showing the asymptotic error distribution result. Two numerical experiments are performed to validate our claims about the optimality of the rate of convergence.

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• Analysis of splitting schemes for stochastic evolution equations with non-Lipschitz nonlinearities driven by fractional noise
• Symplectic methods for stochastic Hamiltonian systems: asymptotic error distributions and Hamiltonian-specific analysis
• Asymptotic error distribution for stochastic Runge--Kutta methods of strong order one

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