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Probability Seminar

Event Type
Department of Mathematics
243 Altgeld Hall
Mar 28, 2023   2:00 - 2:50 pm  
Cheng Ouyang (UIC, Math)

Title: Colored noise and parabolic Anderson model on Torus  

Abstract: We construct an intrinsic family of Gaussian noises on compact Riemannian manifolds, which we call the colored noise on manifolds. It consists of noises with a wide range of singularities. This family of noises allows the study of the parabolic Anderson model (PAM) on compact manifolds in high dimensions in the Ito sense. We started our investigation on a toy model, an n-dimensional torus, and established the existence and uniqueness of the solution, as well as some sharp bounds on the second moment of the solution. It sheds light to the study of PAM on more general manifolds.

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