Differentiation formula in Stratonovich version for fractional Brownian sheet

Abstract

We introduce two types of the Stratonovich stochastic integrals for two-parameter processes, and investigate the relationship of these Stratonovich integrals and various types of Skorohod integrals with respect to a fractional Brownian sheet. By using this relationship. we derive a differentiation formula in the Stratonovich sense for fractional Brownian sheet through Ito formula. Also the relationship between the two types of the Stratonovich integrals will be obtained and used to derive a differentiation formula in the Stratonovich sense. In this case. our proof is based on the repeated applications of differentiation formulas in the Stratonovich form for one-parameter Gaussian processes. (C) 2009 Elsevier Inc. All rights reserved.