The Milstein scheme for stochastic delay differential equations without using anticipative calculus

Tony Shardlow, Peter Kloeden

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)
184 Downloads (Pure)

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 differential equa-
tions 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 first order strong
rate of convergence for stochastic delay differential equations.
Original languageEnglish
Pages (from-to)181-202
Number of pages21
JournalStochastic Analysis and Applications
Volume30
Issue number2
DOIs
Publication statusPublished - 2012

Keywords

  • stochastic equations
  • delay equation
  • numerical analysis

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