Skorohod and Stratonovich integration in the plane

Khalil Chouk (1) , Samy Tindel (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 BIGS - Biology, genetics and statistics

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 indexed by a square, 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 the suqare. (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.

Mots clés: Malliavin calculus; Stochastic integral; Rough path; Young integrals

Domaines: Probabilités [math.PR]

Khalil Chouk, Samy Tindel. Skorohod and Stratonovich integration in the plane. Electronic Journal of Probability, 2015, 20, no 39, 50 pp. ⟨hal-00866067⟩