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

  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.},
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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    The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
  • 1977
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