Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

@article{Higham2002StrongCO,
  title={Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations},
  author={Desmond J. Higham and Xuerong Mao and Andrew M. Stuart},
  journal={SIAM J. Numer. Anal.},
  year={2002},
  volume={40},
  pages={1041-1063}
}
Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients. In practice, many important SDE models satisfy only a local Lipschitz property and, since Brownian paths can make arbitrarily large excursions, the global Lipschitz-based theory is not directly relevant. In this work we prove strong convergence results under less restrictive conditions. First, we give… 
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