Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

Raluca M. Balan () and Ciprian A. Tudor ()
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Raluca M. Balan: University of Ottawa
Ciprian A. Tudor: Université de Panthéon-Sorbonne Paris 1

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 834-870

Abstract: Abstract We consider the stochastic heat equation with multiplicative noise $u_{t}=\frac{1}{2}\Delta u+u\dot{W}$ in ℝ+×ℝ d , whose solution is interpreted in the mild sense. The noise $\dot{W}$ is fractional in time (with Hurst index H≥1/2), and colored in space (with spatial covariance kernel f). When H>1/2, the equation generalizes the Itô-sense equation for H=1/2. We prove that if f is the Riesz kernel of order α, or the Bessel kernel of order α 1/2), respectively d

Keywords: Stochastic heat equation; Gaussian noise; Multiple stochastic integrals; Chaos expansion; Skorohod integral; Fractional Brownian motion; Local time; 60H15; 60H05 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0237-3

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