Electronic Journal of Probability

Skorohod and Stratonovich integration in the plane

Khalil Chouk and Samy Tindel

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This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path $x:[0,1]^{2}\to\mathbb{R}$ satisfying some Hölder regularity conditions with a Hölder exponent greater than $1/3$. (ii) Get some Skorohod change of variable formulas for a large class of Gaussian processes defined on $[0,1]^{2}$. (iii) Compare the bidimensional integrals obtained with those two methods, computing explicit correction terms whenever possible. As a byproduct, we also give explicit forms of corrections in the respective change of variable formulas.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 39, 39 pp.

Accepted: 8 April 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G15: Gaussian processes 60G22: Fractional processes, including fractional Brownian motion

Young integrals Rough path Stochastic integral Malliavin calculus

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Chouk, Khalil; Tindel, Samy. Skorohod and Stratonovich integration in the plane. Electron. J. Probab. 20 (2015), paper no. 39, 39 pp. doi:10.1214/EJP.v20-3041. https://projecteuclid.org/euclid.ejp/1465067145

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