A quasilinear stochastic partial differential equation driven by fractional white noise

Wilfried Grecksch; Christian Roth

doi:10.1515/mcma.2007.019

Published by De Gruyter February 13, 2008

A quasilinear stochastic partial differential equation driven by fractional white noise

Wilfried Grecksch and Christian Roth

From the journal Monte Carlo Methods and Applications

https://doi.org/10.1515/mcma.2007.019

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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 Analysis12 (2000), 385–401] who used it in the pure Brownian motion case.

Keywords: Fractional Brownian motion; fractional white noise; Gjessing's lemma; SPDE

Received: 2007-06-07

Revised: 2007-11-15

Published Online: 2008-02-13

Published in Print: 2008-01

A quasilinear stochastic partial differential equation driven by fractional white noise

Abstract

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