Tuesday, September 15, 2009
03:30 PM in REC 113
Lucian Beznea
Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Tightness of capacities, compact superharmonic functions, and path regularity

Abstract

We discuss the relations between the existence of the L-superharmonic functions that have compact level sets (L being the generator of a right Markov process), the path regularity of the process, and the tightness of the induced capacities. We present several examples, mainly in infinite dimensional situations, like the case when L is the Gross-Laplace operator on an abstract Wiener space. We deduce the còadlòag property of the paths of a class of measure-valued branching process associated with nonlinear operators of the form Lu+ ö(u), where ö is "branching mechanism".

The talk includes results from joint works with Nicu Boboc and Michael Röckner.