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

On the convergence order of the Euler scheme for scalar SDEs with H\"older-type diffusion coefficients