Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
Weak convergence of Euler-type methods for numerical integration of ordinary stochastic differential equations with one-sided Lipschitz continuous drift and global Lipschitz continuous diffusion terms is verified. Some simulation results are given as well. For strong convergence, see \textit{H. Schurz} [Int. J. Numer. Anal. Model. 3, No. 4, 459--480 (2006; Zbl 1109.65010)] where similar examples are discussed and strong convergence is established by an axiomatic approach.
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