Journal article
Spatial averages for the parabolic Anderson model driven by rough noise
Alea (2006), v 18(1), pp 907-943
01 Jan 2021
Abstract
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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Details
- Title
- Spatial averages for the parabolic Anderson model driven by rough noise
- Creators
- David Nualart - Univ Kansas, Dept Math, 1460 Jayhawk Blvd, Lawrence, KS 66045 USAXiaoming Song - Drexel UniversityGuangqu Zheng - Univ Kansas, Dept Math, 1460 Jayhawk Blvd, Lawrence, KS 66045 USA
- Publication Details
- Alea (2006), v 18(1), pp 907-943
- Publisher
- Impa
- Number of pages
- 37
- Grant note
- 1811181 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000640205300011
- Scopus ID
- 2-s2.0-85105819132
- Other Identifier
- 991019167634804721
InCites Highlights
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Statistics & Probability