Harmonic analysis of additive Levy processes
| dc.creator | Khoshnevisan, Davar | |
| dc.creator | Xiao, Yimin | |
| dc.date | 2007-06-28 | |
| dc.date.accessioned | 2026-07-07T08:12:51Z | |
| dc.date.available | 2026-07-07T08:12:51Z | |
| dc.description | Let $X_1,...,X_N$ denote $N$ independent $d$-dimensional Lévy 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 Lévy processes. We present a few new consequences here. | |
| dc.description | submitted; 54 pages | |
| dc.identifier | https://arxiv.org/abs/0706.4164 | |
| dc.identifier | http://arxiv.org/abs/0706.4164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132598 | |
| dc.subject | Probability | |
| dc.subject | 60G60, 60J55, 60J45 | |
| dc.title | Harmonic analysis of additive Levy processes | |
| dc.type | text |