Stratonovich Calculus with Respect to Fractional Brownian Sheet

Abstract

We introduce two types of Stratonovich stochastic integrals for two-parameter process. The relationship of Stratonovich integrals to Skorohod integrals will be investigated. By using this relationship, we prove that a differentiation formula for fractional Brownian sheet in Stratonovich form can be expressed as the sum of Stratonovich integrals of two types introduced in this article.

Keywords:

• Fractional Brownian sheet
• Itô formula
• Malliavin calculus
• Skorohod integrals
• Stratonovich stochastic integrals

Mathematics Subject Classification:

• Primary 60H07
• Secondary 60G18

This work was supported by KRF Grant KRF-2007-311-C00127 and KRF-2007-412-J02303.