On the convergence order of the Euler scheme for scalar SDEs with Hölder-type diffusion coefficients

2023/07/21 by Mickel, Annalena, Neuenkirch, Andreas
#60H35 #65C30 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.11448

Abstract

We study the Euler scheme for scalar non-autonomous stochastic differential equations, whose diffusion coefficient is not globally Lipschitz but a fractional power of a globally Lipschitz function. We analyse the strong error and establish a criterion, which relates the convergence order of the Euler scheme to an inverse moment condition for the diffusion coefficient. Our result in particular applies to Cox-Ingersoll-Ross-, Chan-Karolyi-Longstaff-Sanders- or Wright-Fisher-type stochastic differential equations and thus provides a unifying framework.

Related

• The Euler scheme for stochastic differential equations with discontinuous drift coefficient: A numerical study of the convergence rate
• An explicit Euler scheme with strong rate of convergence for financial\n SDEs with non-Lipschitz coefficients
• Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient
• Weak convergence analysis of the symmetrized Euler scheme for one dimensional SDEs with diffusion coefficient |x|^a, a in [1/2,1)
• Backward Euler method for stochastic differential equations with non-Lipschitz coefficients