Mathematics Colloquium
Spring 2010
Zhen-Qing Chen
University of Washington
Global Heat Kernel Estimates for Jump-Diffusions
In this talk, I will describe recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric discontinuous processes (or equivalently, a class of symmetric integro-differential operators). A prototype of the Markov processes under consideration is the mixture of symmetric diffusion of uniformly elliptic divergence form operator and symmetric stable-like processes on $R^d$. I will focus on the sharp two-sided estimates for the transition density functions (or heat kernels) of the processes, while briefly mention a priori Holder estimates and parabolic Harnack inequalities for their parabolic functions. To establish these results, we have employed methods from both probability theory and analysis. Based on joint work with Takashi Kumagai.