An Itô Formula of Generalized Functionals and Local Time for Fractional Brownian Sheet

Abstract

By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameters H ₁, H ₂ ∈ (0,1). As an application, we give the integral representations for two versions of local times of a fractional Brownian sheet, respectively.

Keywords:

• Donsker's delta function
• Fractional Brownian sheet
• Itô formula
• Local time
• White noise theory

Mathematics Subject Classification:

• Primary 60H05
• Secondary 60H04

ACKNOWLEDGMENT

This research was supported (in part) by KRF Grant R05-2004-000-11516-0.