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Spatial averages for the parabolic Anderson model driven by rough noise
Journal article   Open access

Spatial averages for the parabolic Anderson model driven by rough noise

David Nualart, Xiaoming Song and Guangqu Zheng
Alea (2006), v 18(1), pp 907-943
01 Jan 2021
url
https://doi.org/10.30757/alea.v18-33View
Published, Version of Record (VoR)Maybe Open Access (Publisher Bronze) Open

Abstract

Mathematics Physical Sciences Science & Technology Statistics & Probability
In this paper, we study spatial averages for the parabolic Anderson model in the Skorohod sense driven by rough Gaussian noise, which is colored in space and time. We include the case of a fractional noise with Hurst parameters H-0 in time and H-1 in space, satisfying H-0 is an element of (1/2, 1), H-1 is an element of (0, 1/2) and H-0 +H-1 > 3/4. Our main result is a functional central limit theorem for the spatial averages. As an important ingredient of our analysis, we present a Feynman-Kac formula that is new for these values of the Hurst parameters.

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Domestic collaboration
Web of Science research areas
Statistics & Probability
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