Numerische Mathematik

, Volume 112, Issue 1, pp 41–64

Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients


DOI: 10.1007/s00211-008-0200-8

Cite this article as:
Jentzen, A., Kloeden, P.E. & Neuenkirch, A. Numer. Math. (2009) 112: 41. doi:10.1007/s00211-008-0200-8


We study the approximation of stochastic differential equations on domains. For this, we introduce modified Itô–Taylor schemes, which preserve approximately the boundary domain of the equation under consideration. Assuming the existence of a unique non-exploding solution, we show that the modified Itô–Taylor scheme of order γ has pathwise convergence order γε for arbitrary ε > 0 as long as the coefficients of the equation are sufficiently differentiable. In particular, no global Lipschitz conditions for the coefficients and their derivatives are required. This applies for example to the so called square root diffusions.

Mathematics Subject Classification (2000)

65C30 60H35 

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Johann Wolfgang Goethe-UniversitätInstitut für MathematikFrankfurt am MainGermany

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