Electronic Communications in Probability

Stein approximation for Itô and Skorohod integrals by Edgeworth type expansions

Nicolas Privault

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Abstract

We derive Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which apply to SDE solutions and to multiple stochastic integrals.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 35, 10 pp.

Dates
Accepted: 25 April 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320962

Digital Object Identifier
doi:10.1214/ECP.v20-3827

Mathematical Reviews number (MathSciNet)
MR3342169

Zentralblatt MATH identifier
1321.60118

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 62E17: Approximations to distributions (nonasymptotic) 60G15: Gaussian processes 60H05: Stochastic integrals

Keywords
Stein method cumulants Malliavin calculus Wiener space Edgeworth expansions It\^o integral Skorohod integral

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

Citation

Privault, Nicolas. Stein approximation for Itô and Skorohod integrals by Edgeworth type expansions. Electron. Commun. Probab. 20 (2015), paper no. 35, 10 pp. doi:10.1214/ECP.v20-3827. https://projecteuclid.org/euclid.ecp/1465320962


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