Skorohod and rough integration for stochastic differential equations driven by Volterra processes
File(s)
Published version
Author(s)
Cass, Thomas
Lim, Nengli
Type
Journal Article
Abstract
Given a solution Y to a rough differential equation (RDE), a recent result [7] extends the classical Ito-Stratonovich formula and provides a closed-form expression for ∫ Y ○ dX − ∫ Y dX, i.e. the difference between the rough and Skorohod integrals of Y with respect to X, where X is a Gaussian process with finite p-variation less than 3. In this paper, we extend this result to Gaussian processes with finite p-variation such that 3 ≤ p < 4. The constraint this time is that we restrict ourselves to Volterra Gaussian processes with kernels satisfying a natural condition, which however still allows the result to encompass many standard examples, including fractional Brownian motion with Hurst parameter H > 1/4. As an application we recover Ito formulas in the case where the vector fields of the RDE governing Y are commutative.
Date Issued
2021-02
Date Acceptance
2020-05-29
Citation
L'Institut Henri Poincare, Annales B: Probabilites et Statistiques, 2021, 57 (1), pp.132-168
ISSN
0246-0203
Publisher
Institute Henri Poincaré
Start Page
132
End Page
168
Journal / Book Title
L'Institut Henri Poincare, Annales B: Probabilites et Statistiques
Volume
57
Issue
1
Copyright Statement
© Association des Publications de l’Institut Henri Poincaré, 2021
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Identifier
https://projecteuclid.org/journals/annales-de-linstitut-henri-poincare-probabilites-et-statistiques/volume-57/issue-1/Skorohod-and-rough-integration-for-stochastic-differential-equations-driven-by/10.1214/20-AIHP1074.short
Grant Number
EP/M00516X/1
BKR01300
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Rough path theory
Volterra processes
Malliavin calculus
CALCULUS
RESPECT
STRATONOVICH
Statistics & Probability
0104 Statistics
Publication Status
Published
Date Publish Online
2021-02