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The Milstein scheme for stochastic delay differential equations without using anticipative calculus
OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/318661e3-2582-4373-91b2-ec545e6e9f54 • DOI: https://doi.org/10.1080/07362994.2012.628907
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.
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.