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On the convergence order of the Euler scheme for scalar SDEs with Hölder-type diffusion coefficients (2307.11448v2)
Published 21 Jul 2023 in math.NA, cs.NA, and math.PR
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.