Potential theory of infinite dimensional Lévy processes

Details Potential theory of infinite dimensional Lévy processes Potential theory of infinite dimensional Lévy processes

2010-07-14

arxiv.org/abs/1007.2379v2

Mathematics

Probability

24 pages

Scientific paper

We study the potential theory of a large class of infinite dimensional L\'evy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e. excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as e.g. formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the L\'evy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.

Affiliated with

Also associated with

No associations

Rating

Potential theory of infinite dimensional Lévy processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Potential theory of infinite dimensional Lévy processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Potential theory of infinite dimensional Lévy processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-121172