This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) ...This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.展开更多
In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arisi...In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.展开更多
基金Research partially supported by the “1000 Talents Plan” from Jilin University,Jilin Province and Chinese Governmentby the Simons Foundation(244767)
文摘This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.
基金supported by the National Natural Science Foundation of China (12201282)the Institute of Meteorological Big Data-Digital Fujian and the Fujian Key Laboratory of Data Science and Statistics (2020L0705)the Education Department of Fujian Province (JAT200325)。
文摘In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.
