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


Reference:

Shardlow, T. and Kloeden, P., 2012. The Milstein scheme for stochastic delay differential equations without using anticipative calculus. Stochastic Analysis and Applications, 30 (2), pp. 181-202.

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    Official URL:

    http://dx.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.

    Details

    Item Type Articles
    CreatorsShardlow, T.and Kloeden, P.
    DOI10.1080/07362994.2012.628907
    Uncontrolled Keywordsstochastic equations, delay equation, numerical analysis
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code32123

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