Asymptotic behavior of the solution of the fractional heat equation

Litan Yan, Xianye Yu and Xichao Sun

Statistics & Probability Letters, 2016, vol. 117, issue C, 54-61

Abstract: In this short note, we study the asymptotic behavior of the solution to the fractional heat equation ∂u∂t(t,x)=−(−Δ)α/2u(t,x)+u(t,x)∂d+1W∂t∂x1⋯∂xd,t>0,x∈Rd with initial condition bounded above and below, where α∈(0,2) and the noise W(t,x) is a fractional Brownian sheet. The method of moments is used to investigate the solution.

Keywords: Fractional heat equation; Fractional Brownian sheet; Asymptotic behavior (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2016.05.004

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