Random fractals determined by Lévy processes
The paper is devoted to various results on Blumenthal-Getoor indices, in particular, it contains a good survey of existing results. A new index \(\eta\) for a Lévy process \(X\) is introduced, \[ \eta:=\sup\Big\{ \alpha>0: \limsup_{a\to 0} a^\alpha ET(a,a)<\infty \Big\}, \] where \(T(a,s)\) is the sojourn time of \(X\) in the ball of radius \(a\), centered at the origin, up to time \(s\). In particular, it is shown that \(\eta\) is equal to the dimension of the graph of \(X\), \(\text{Gr}(X, \mathbb R_+):=\{(t,X(t)): t\in \mathbb R_+\}\).
scientific article; zbMATH DE number 5833864
scientific article