Skorohod and Stratonovich integration in the plane

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.