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)


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
Issue number4
Publication statusPublished - 2012 Apr


  • 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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