Speaker: Li Chen, Louisiana State University

Title: Fractional Gaussian fields and Parabolic Anderson Models on the Sierpinski gasket

 

Abstract: We will first introduce fractional Gaussian fields and their regularity properties on the Sierpinski gasket. Namely, such fields are defined as distributions \(X_{\alpha} = (-\Delta)^{-\alpha}W\), where \(W\) is a Gaussian white noise and \(\Delta\) is the Laplacian. Then we will discuss Parabolic Anderson Models  \({\partial_t} u=\Delta u+\beta u\dot{W}_{\alpha}\), where the fractional noise is white in time and \(X_{\alpha}\) in space. We will study the existence and uniqueness of solutions in the Ito sense and give their moment estimates. The main analytic tools are heat kernel estimates and spectral theory.

 

Host: Erkan Nane