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2015 Skorohod and Stratonovich integration in the plane
Khalil Chouk, Samy Tindel
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Electron. J. Probab. 20: 1-39 (2015). DOI: 10.1214/EJP.v20-3041

Abstract

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.

Citation

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Khalil Chouk. Samy Tindel. "Skorohod and Stratonovich integration in the plane." Electron. J. Probab. 20 1 - 39, 2015. https://doi.org/10.1214/EJP.v20-3041

Information

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

zbMATH: 1322.60081
MathSciNet: MR3335830
Digital Object Identifier: 10.1214/EJP.v20-3041

Subjects:
Primary: 60H07
Secondary: 60G15, 60G22

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