Riemann-Skorohod and Stratonovich integrals for Gaussian processes

Abstract

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 $\ddot{I}$-variation for $\ddot{I}\ge 1$ and that the diagonals of covariance functions are of finite $\ddot{I}{}^{\prime }$-variation for $\ddot{I}{}^{\prime }\ge 1$ such that $\frac{1}{\ddot{I}{}^{\prime }}+\frac{1}{2\ddot{I}}>1$. 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 $[\ddot{I}]$-th order Skorohod-Riemann sum.

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