Harmonic analysis of additive Levy processes

Details Harmonic analysis of additive Levy processes Harmonic analysis of additive Levy processes

2007-06-28

arxiv.org/abs/0706.4164v1

Mathematics

Probability

submitted; 54 pages

Scientific paper

Let $X_1,...,X_N$ denote $N$ independent $d$-dimensional L\'evy processes, and consider the $N$-parameter random field \[\X(\bm{t}):= X_1(t_1)+...+X_N(t_N).\] First we demonstrate that for all nonrandom Borel sets $F\subseteq\R^d$, the Minkowski sum $\X(\R^N_+)\oplus F$, of the range $\X(\R^N_+)$ of $\X$ with $F$, can have positive $d$-dimensional Lebesgue measure if and only if a certain capacity of $F$ is positive. This improves our earlier joint effort with Yuquan Zhong \ycite{KXZ:03} by removing a symmetry-type condition there. Moreover, we show that under mild regularity conditions, our necessary and sufficient condition can be recast in terms of one-potential densities. This rests on developing results in classical [non-probabilistic] harmonic analysis that might be of independent interest. As was shown in \fullocite{KXZ:03}, the potential theory of the type studied here has a large number of consequences in the theory of L\'evy processes. We present a few new consequences here.

Affiliated with

Also associated with

No associations

Rating

Harmonic analysis of additive Levy 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 Harmonic analysis of additive Levy processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Harmonic analysis of additive Levy processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-456329