THE MILSTEIN SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITHOUT ANTICIPATIVE CALCULUS

Kloeden, P.E. and Shardlow, T. (2010) THE MILSTEIN SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITHOUT ANTICIPATIVE CALCULUS. [MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 41 Approximations and expansions MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	24 Aug 2010
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1514

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