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Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift

Foroush Bastani, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.cam.2011.10.023
  3. Publisher: 2012
  4. Abstract:
  5. In this paper, we are concerned with the numerical approximation of stochastic differential equations with discontinuous/nondifferentiable drifts. We show that under one-sided Lipschitz and general growth conditions on the drift and global Lipschitz condition on the diffusion, a variant of the implicit Euler method known as the split-step backward Euler (SSBE) method converges with strong order of one half to the true solution. Our analysis relies on the framework developed in [D. J. Higham, X. Mao and A. M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM Journal on Numerical Analysis, 40 (2002) 10411063] and exploits the relationship which exists between explicit and implicit Euler methods to establish the convergence rate results
  6. Keywords:
  7. Non-smooth drift ; Euler-Maruyama method ; Non-smooth ; One-sided Lipschitz condition ; Split-step backward Euler method ; Stochastic differential equations ; Differential equations ; Differentiation (calculus) ; Euler equations ; Nonlinear equations ; Numerical analysis ; Stochastic systems ; Convergence of numerical methods
  8. Source: Journal of Computational and Applied Mathematics ; Volume 236, Issue 7 , 2012 , Pages 1903-1918 ; 03770427 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S037704271100570X