期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2021
卷号：18
期号：1
页码：907
DOI：10.30757/ALEA.v18-33
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：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 H0 in time and H1 in space, satisfying H0 ∈ (1/2, 1), H1 ∈ (0, 1/2) and H0 H1 > 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.
其他关键词：. Parabolic Anderson model, fractional rough noise, Malliavin calculus, central limit theorem, Wiener chaos expansion, Feynman-Kac formula, fourth moment theorems.
