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arxiv 2205.13659 v1 pith:KKPGUAVP submitted 2022-05-26 math.NA cs.NA

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

classification math.NA cs.NA
keywords backwardeulerdifferentialequationsmethodratestochasticasymptotic
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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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