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Bibliographic Details
Main Author: Liu, Yanghui
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.06983
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author Liu, Yanghui
author_facet Liu, Yanghui
contents In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $ρ$-variation for $ρ\geq 1$ and that the diagonals of covariance functions are of finite $ρ'$-variation for $ρ'\geq 1$ such that $\frac{1}{ρ'}+\frac{1}{2ρ}>1$. The difference between the two types of integrals is identified with a Young integral. We also show that the Skorohod integral is the limit of a $[ρ]$-th order Skorohod-Riemann sum.
format Preprint
id arxiv_https___arxiv_org_abs_2502_06983
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Riemann-Skorohod and Stratonovich integrals for Gaussian processes
Liu, Yanghui
Probability
60H07, 60L20
In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $ρ$-variation for $ρ\geq 1$ and that the diagonals of covariance functions are of finite $ρ'$-variation for $ρ'\geq 1$ such that $\frac{1}{ρ'}+\frac{1}{2ρ}>1$. The difference between the two types of integrals is identified with a Young integral. We also show that the Skorohod integral is the limit of a $[ρ]$-th order Skorohod-Riemann sum.
title Riemann-Skorohod and Stratonovich integrals for Gaussian processes
topic Probability
60H07, 60L20
url https://arxiv.org/abs/2502.06983