抛物Anderson模型（PAM）源于对物理现象的描述，在许多其它方向有重要应用。目前研究其解的长时渐近性质成为概率论中的一个新的研究方向。本项目拟利用概率极限理论、随机偏微分方程、随机矩阵、极值理论、傅里叶分析等相关工具研究抛物Anderson模型解的各种长时渐近性质。主要研究内容包括：(a) 各种随机势函数下PAM解存在性、唯一性、连续性等性质； (b) PAM解的分布性质； (c) 分数抛物Anderson模型解的李雅普诺夫指数矩的渐近性质；(d) PAM解的精确渐近性、重对数律等极限定理。

The parabolic Anderson model (PAM) is derived from the description of physical phenomena and has important applications in many other directions. At present, the study of the long term asymptotic behavior of the solution becomes a new research direction in probability theory. In this project, we use the probability limit theory, stochastic partial differential equation, random matrix, extreme value theory, Fourier analysis and other related tools to study the long term asymptotic behavior of solutions of parabolic Anderson model. In particular, we shall study : (a) the existence, uniqueness, continuity for the mild solutions and weak solutions under different potentials, (b) the distributional properties for the solutions of the models, (c) the precise moment Lyapunov exponent for the solutions of the fractional Parabolic Anderson Model , (d) the limit theorems such as precise asymptotics, law of the iterated logarithm of the model’s solutions.