A note on intermittency for the fractional heat equation

Raluca M. Balan and Daniel Conus

Statistics & Probability Letters, 2014, vol. 95, issue C, 6-14

Abstract: The goal of the present note is to study intermittency properties for the solution to the fractional heat equation ∂u∂t(t,x)=−(−Δ)β/2u(t,x)+u(t,x)Ẇ(t,x),t>0,x∈Rd with initial condition bounded above and below, where β∈(0,2] and the noise W behaves in time like a fractional Brownian motion of index H>1/2, and has a spatial covariance given by the Riesz kernel of index α∈(0,d). As a by-product, we obtain that the necessary and sufficient condition for the existence of the solution is α<β.

Keywords: Fractional heat equation; Fractional Brownian motion; Malliavin calculus; Intermittency (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spl.2014.08.001

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