An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process

By Steffen Dereich, Andreas Neuenkirch, Lukasz Szpruch. Proceedings of the Royal Society A, 2012

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Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process (2013, methodology): “Different ad-hoc discretization schemes have thus been proposed in the literature (see references in [2]).”
Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations (2013, background): “In the case ρ0, η1 ∈ [β4 ,∞) the processes arcsin( √ Xx), x ∈ (0,∞), satisfy an SDE with constant diffusion function and non-increasing drift function; see, e.g., Neuenkirch & Szpruch [36].”
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”