Harnack Inequalities and Bounds for Densities of Stochastic Processes

Abstract

We consider possibly degenerate parabolic operators in the form L = m k=1 *

A survey on the classical theory for Kolmogorov equation

“…In particular, a first application of this tool can be found in the proof of Proposition 4.9 in the following subsection, where Harnack chains are used to prove a geometric version of Theorem 4.3. Further applications can be found in the papers by Polidoro [61], Di Francesco and Polidoro [30], Boscain and Polidoro [14] and Cibelli and Polidoro [19] to obtain asymptotic estimates for the fundamental solution. We also recall the work by Cinti, Nyström and Polidoro [21,22] where a boundary Harnack inequality is proved.…”