Electronic Journal of Probability

Probability approximation by Clark-Ocone covariance representation

Nicolas Privault and Giovanni Luca Torrisi

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Abstract

Based on the Stein method and a general integration by parts framework we derive various bounds on the distance between probability measures. We show that this framework can be implemented on the Poisson space by covariance identities obtained from the Clark-Ocone representation formula and derivation operators. Our approach avoids the use of the inverse of the Ornstein Uhlenbeck operator as in the existing literature, and also applies to the Wiener space.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 91, 25 pp.

Dates
Accepted: 23 October 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064316

Digital Object Identifier
doi:10.1214/EJP.v18-2787

Mathematical Reviews number (MathSciNet)
MR3126574

Zentralblatt MATH identifier
1308.60069

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G57: Random measures 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Poisson space Stein-Chen method Malliavin calculus Clark-Ocone formula

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Privault, Nicolas; Torrisi, Giovanni Luca. Probability approximation by Clark-Ocone covariance representation. Electron. J. Probab. 18 (2013), paper no. 91, 25 pp. doi:10.1214/EJP.v18-2787. https://projecteuclid.org/euclid.ejp/1465064316


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