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

Seiichiro Kusuoka, Ciprian A. Tudor

Research output: Contribution to journalArticle

21 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 1 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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