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

Seiichiro Kusuoka; Ciprian A. Tudor

doi:10.1016/j.spa.2012.02.005

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

Seiichiro Kusuoka, Ciprian A. Tudor

Research output: Contribution to journal › Article › peer-review

24 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 language	English
Pages (from-to)	1627-1651
Number of pages	25
Journal	Stochastic Processes and their Applications
Volume	122
Issue number	4
DOIs	https://doi.org/10.1016/j.spa.2012.02.005
Publication status	Published - 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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10.1016/j.spa.2012.02.005

Cite this

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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.}",

note = "Funding Information: The second author was partially supported by the ANR grant “Masterie” BLAN 012103 . Associate member of the team Samos, Universit{\'e} de Panth{\'e}on-Sorbonne Paris 1. This work has been partially completed when the second author has visited Keio University. He acknowledges generous support from Japan Society for the Promotion of Science. ",

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

AU - Kusuoka, Seiichiro

AU - Tudor, Ciprian A.

N1 - Funding Information: The second author was partially supported by the ANR grant “Masterie” BLAN 012103 . Associate member of the team Samos, Université de Panthéon-Sorbonne Paris 1. This work has been partially completed when the second author has visited Keio University. He acknowledges generous support from Japan Society for the Promotion of Science.

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

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 4

ER -

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

Abstract

Keywords

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