The linear Steklov method for SDEs with non-globally Lipschitz coefficients: Strong convergence and simulation

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• 作者：S. Dí ; az-Infante ^{sauld@cimat.mx" class="auth_mail" title="E-mail the corresponding author} ; S. Jerez ; ^{jerez@cimat.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Stochastic differential equations ; Explicit methods ; Strong convergence ; Steklov average
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：408-423
• 全文大小：739 K

文摘

We present an explicit numerical method for solving stochastic differential equations with non-globally Lipschitz coefficients. A linear version of the Steklov average under a split-step formulation supports our new solver. The linear Steklov method converges strongly with a standard one-half order. Also, we present numerical evidence that the explicit linear Steklov reproduces almost surely stability solutions with high-accuracy for diverse application models even for stochastic differential systems with super-linear diffusion coefficients.