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2010.77: THE MILSTEIN SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITHOUT ANTICIPATIVE CALCULUS

2010.77: P.E. Kloeden and T. Shardlow (2010) THE MILSTEIN SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITHOUT ANTICIPATIVE CALCULUS.

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Abstract

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay dierential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This paper employs an elementary method to derive the Milstein scheme and its rst order strong rate of convergence for stochastic delay dierential equations.

Item Type:MIMS Preprint
Uncontrolled Keywords:Taylor expansions, stochastic dierential equations, delay equations, strong convergence, SDDE, Milstein method
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 41 Approximations and expansions
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 65 Numerical analysis
MIMS number:2010.77
Deposited By:Ms Lucy van Russelt
Deposited On:24 August 2010

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