Multiparameter Fractional Brownian Motion And Quasi-Linear Stochastic Partial Differential Equations

Abstract

We develop a multiparameter white noise theory for fractional Brownian motion with Hurst multiparameter The theory is used to solve the linear and a quasi-linear heat equation driven by multiparameter fractional white noise. It is proved that for some values of H(depending on the dimension) the solution has a jointly continuous version in t and x