Abstract
Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an Itô formula for the fractional Brownian sheet with Hurst parameters bigger than $1/2$. As an application, we give a stochastic integral representation for the local time of the fractional Brownian sheet.
Highlights
Let (Btα)t∈[0,1] be the fractional Brownian motion with Hurst parameter α ∈ (0, 1)
The aim of this paper is to develop a stochastic calculus for the two-parameter fBm introduced in [3], known as the fractional Brownian sheet
As an application we study the representation of the local time of the fractional Brownian sheet in terms of Skorohod stochastic integrals
Summary
Let (Btα)t∈[0,1] be the fractional Brownian (fBm) motion with Hurst parameter α ∈ (0, 1). The aim of this paper is to develop a stochastic calculus for the two-parameter fBm introduced in [3], known as the fractional Brownian sheet. As an application we study the representation of the local time of the fractional Brownian sheet in terms of Skorohod stochastic integrals. Our paper is organized as follows: Section 2 contains the basic notions of the Malliavin calculus for Gaussian processes and the definition of the fractional Brownian sheet.
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