The rates of the Lp-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition

Shigeki Aida, Takanori Kikuchi, Seiichiro Kusuoka

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider the rates of the Lp-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition on the coefficients. By a transformation, the stochastic differential equations of Markovian type with reflecting boundary condition on sufficiently good domains are to be associated with the equations concerned in the present paper. The obtained rates of the Lp-convergence are the same as those in the case of the stochastic differential equations of Markovian type without boundaries.

    Original languageEnglish
    Pages (from-to)65-95
    Number of pages31
    JournalTohoku Mathematical Journal
    Volume70
    Issue number1
    DOIs
    Publication statusPublished - Mar 2018

    Keywords

    • Euler-maruyama approximation
    • Path-dependent coefficient
    • Rate of convergence
    • Reflecting boundary condition
    • Stochastic differential equation
    • Wong-Zakai approximation

    ASJC Scopus subject areas

    • Mathematics(all)

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