A remark on a result of Xia Chen

We consider the parabolic Anderson model which is driven by a Gaussian noise fractional in time and having certain scaling property in the spatial variables. Recently, Xia Chen has obtained exact Lyapunov exponent for all moments of positive integer orders. In this note, we explain how to extend Xia...

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Bibliographic Details
Published inStatistics & probability letters Vol. 118; pp. 124 - 126
Main Author Lê, Khoa
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2016
Subjects
Feynman–Kac’s representation
Hypercontractivity
Parabolic Anderson
Parabolic Anderson
Hypercontractivity
Feynman–Kac’s representation
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Summary:We consider the parabolic Anderson model which is driven by a Gaussian noise fractional in time and having certain scaling property in the spatial variables. Recently, Xia Chen has obtained exact Lyapunov exponent for all moments of positive integer orders. In this note, we explain how to extend Xia Chen’s result for all moments of order p, where p is any real number at least 2.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2016.06.004