A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients

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An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process (2012, methodology): “Strong convergence (without a rate or with a logarithmic rate) of several discretization schemes has been shown by Deelstra & Delbaen (1998), Alfonsi (2005), Higham & Mao (2005), Bossy & Diop (2007) and Gyöngy & Rásonyi (2011).”
Loss of regularity for Kolmogorov equations (2012, background): “Strong and numerically weak convergence rates without assuming global monotonicity are established in Göngy & Rasonyi [26] in the case of a class of scalar SDEs with globally Hölder continuous coefficients, in Dörsek [14] in the case of the two-dimensional stochastic Navier-Stokes equations and i”