DMS Stochastic Analysis Seminar (SASA)

Speaker: Cheng Ouyang, University of Illinois, Chicago, 

Title: Parabolic Anderson Models in Sierpinski Gasket

Abstract: We study the parabolic Anderson model (PAM) on fractals such as the Sierpinski gasket. Besides proving existence and uniqueness of the solution in the Ito sense, we also obtain precise \(L^p\) estimates for the solution which leads to intermittency properties. Moreover, our results can be generalized to PAM on bounded domains of recurrent metric measure spaces. It covers a large variety of spaces. In particular, our result further clarifies the picture on a near-dichotomy behavior for the energy of the solution discovered by Khoshnevisan et al.