Citation

BibTex format

@article{Cass:2019:10.1214/18-AOP1254,
author = {Cass, T and Lim, N},
doi = {10.1214/18-AOP1254},
journal = {Annals of Probability},
pages = {1--60},
title = {A Stratonovich-Skorohod integral formula for Gaussian rough paths},
url = {http://dx.doi.org/10.1214/18-AOP1254},
volume = {47},
year = {2019}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - Given a Gaussian process X, its canonical geometric rough path lift X, and a solution Y to the rough differential equation (RDE) dYt=V(Yt)dXt, we present a closed-form correction formula for ∫YdX−∫YdX, that is, the difference between the rough and Skorohod integrals of Y with respect to X. When X is standard Brownian motion, we recover the classical Stratonovich-to-Itô conversion formula, which we generalize to Gaussian rough paths with finite p-variation, p<3, and satisfying an additional natural condition. This encompasses many familiar examples, including fractional Brownian motion with H>13. To prove the formula, we first show that the Riemann-sum approximants of the Skorohod integral converge in L2(Ω) by using a novel characterization of the Cameron–Martin norm in terms of higher-dimensional Young–Stieltjes integrals. Next, we append the approximants of the Skorohod integral with a suitable compensation term without altering the limit, and the formula is finally obtained after a rebalancing of terms.
AU - Cass,T
AU - Lim,N
DO - 10.1214/18-AOP1254
EP - 60
PY - 2019///
SN - 0091-1798
SP - 1
TI - A Stratonovich-Skorohod integral formula for Gaussian rough paths
T2 - Annals of Probability
UR - http://dx.doi.org/10.1214/18-AOP1254
UR - http://arxiv.org/abs/1604.06846v2
UR - http://hdl.handle.net/10044/1/56747
VL - 47
ER -