A quasilinear stochastic partial differential equation driven by fractional white noise

Abstract

The objective of the paper is to give the representation of a solution of a quasilinear stochastic partial differential equation driven by scalar fractional Brownian motion B H ( t ), H ∈ (½, 1), in the white noise framework for fractional Brownian motion. The solution is represented as a Wick product between a fractional Wick exponential and the solution of a path wise deterministic parabolic partial differential equation. Thereby a fractional theory of fractional translation operators is developed and used in the spirit of Benth and Gjessing [F. E. Benth and H. Gjessing. A nonlinear parabolic equation with noise. Potential Analysis 12 (2000), 385–401] who used it in the pure Brownian motion case.