Electronic Communications in Probability

Stein approximation for Itô and Skorohod integrals by Edgeworth type expansions

Nicolas Privault

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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

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

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

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Zentralblatt MATH identifier

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

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

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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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