Stein's method for invariant measures of diffusions via Malliavin calculus

Seiichiro Kusuoka, Ciprian A. Tudor

    Research output: Contribution to journalArticlepeer-review

    23 Citations (Scopus)

    Abstract

    Given a random variable F regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and any probability measure with a density function which is continuous, bounded, strictly positive on an interval in the real line and admits finite variance. The bounds are given in terms of the Malliavin derivative of F. Our approach is based on the theory of It diffusions and the stochastic calculus of variations. Several examples are considered in order to illustrate our general results.

    Original languageEnglish
    Pages (from-to)1627-1651
    Number of pages25
    JournalStochastic Processes and their Applications
    Volume122
    Issue number4
    DOIs
    Publication statusPublished - Apr 2012

    Keywords

    • Berry-Esséen bounds
    • Diffusions
    • Invariant measure
    • Malliavin calculus
    • Multiple stochastic integrals
    • Stein's method
    • Weak convergence

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

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