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

Seiichiro Kusuoka, Ciprian A. Tudor

Research output: Contribution to journalArticle

17 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
Externally publishedYes

Fingerprint

Malliavin Derivative
Stein's Method
Malliavin Calculus
Stochastic Calculus
Strictly positive
Calculus of variations
Random variables
Invariant Measure
Real Line
Density Function
Probability density function
Probability Measure
Random variable
Derivatives
Interval

Keywords

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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Stein's method for invariant measures of diffusions via Malliavin calculus. / Kusuoka, Seiichiro; Tudor, Ciprian A.

In: Stochastic Processes and their Applications, Vol. 122, No. 4, 04.2012, p. 1627-1651.

Research output: Contribution to journalArticle

Kusuoka, Seiichiro ; Tudor, Ciprian A. / Stein's method for invariant measures of diffusions via Malliavin calculus. In: Stochastic Processes and their Applications. 2012 ; Vol. 122, No. 4. pp. 1627-1651.
@article{ef92dea484784a2b8133f8470688bf48,
title = "Stein's method for invariant measures of diffusions via Malliavin calculus",
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.",
keywords = "Berry-Ess{\'e}en bounds, Diffusions, Invariant measure, Malliavin calculus, Multiple stochastic integrals, Stein's method, Weak convergence",
author = "Seiichiro Kusuoka and Tudor, {Ciprian A.}",
year = "2012",
month = "4",
doi = "10.1016/j.spa.2012.02.005",
language = "English",
volume = "122",
pages = "1627--1651",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "4",

}

TY - JOUR

T1 - Stein's method for invariant measures of diffusions via Malliavin calculus

AU - Kusuoka, Seiichiro

AU - Tudor, Ciprian A.

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - Berry-Esséen bounds

KW - Diffusions

KW - Invariant measure

KW - Malliavin calculus

KW - Multiple stochastic integrals

KW - Stein's method

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=84857936163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857936163&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2012.02.005

DO - 10.1016/j.spa.2012.02.005

M3 - Article

AN - SCOPUS:84857936163

VL - 122

SP - 1627

EP - 1651

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 4

ER -