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Euler scheme for SDEs with non-lipschitz diffusion coefficient: Strong convergence. (English) Zbl 1183.65004
Summary: We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |x| α , α[1/2,1). In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
MSC:
65C30Stochastic differential and integral equations
60H35Computational methods for stochastic equations
60H10Stochastic ordinary differential equations
60H35Computational methods for stochastic equations
34F05ODE with randomness
65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE