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Strong convergence of Euler-type methods for nonlinear stochastic differential equations. (English) Zbl 1026.65003

The authors prove the strong convergence of Euler-type methods for nonlinear stochastic differential equations under less restrictive conditions than global Lipschitz-based theory. These less restrictive conditions include the diffusion coefficient being globally Lipschitz and the drift coefficient being Lipschitz under a one-sided condition.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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