A quasilinear stochastic partial differential equation driven by fractional white noise

Grecksch Wilfried and Roth Christian
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Grecksch Wilfried: Martin-Luther-University of Halle-Wittenberg, Department for Mathematics and Computer Sciences, Institute for Optimization and Stochastics, 06099 Halle (Saale), Germany.
Roth Christian: Martin-Luther-University of Halle-Wittenberg, Department for Mathematics and Computer Sciences, Institute for Optimization and Stochastics, 06099 Halle (Saale), Germany. Email: christian.roth@mathematik.uni-halle.de

Monte Carlo Methods and Applications, 2008, vol. 13, issue 5-6, 353-367

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 BH(t), H ∈ (1/2, 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 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1515/mcma.2007.019

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