DMS Analysis and Stochastic Analysis Seminar

Time: Oct 18, 2023 (11:00 AM)
Location: 326 Parker Hall

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