Journal
STOCHASTIC ANALYSIS AND APPLICATIONS
Volume 30, Issue 2, Pages 181-202Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/07362994.2012.628907
Keywords
Delay equations; Milstein method; SDDE; Stochastic differential equations; Strong convergence; Taylor expansions
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Funding
- ARC (UK)
- DAAD (Germany)
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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 differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This article employs an elementary method to derive the Milstein scheme and its first order strong rate of convergence for stochastic delay differential equations.
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