Local Times of Additive Lévy Processes

Abstract

Let X = {X(t); t ∈ R+} be an additive Lévy process in R with X(t) = X1(t1) + · · ·+ XN (tN ), ∀t ∈ R+ , where X1, · · · , XN are independent, classical Lévy processes on R with Lévy exponents Ψ1, . . . , ΨN respectively. Under mild regularity conditions on the Ψi’s, we derive moment estimates that imply joint continuity of the local times in question. These results are then refined to precise estimates for the local and uniform moduli of continuity of local times when all of the Xi’s are strictly stable processes with the same index α ∈ (0, 2]. Running Title Additive Lévy Processes

Cite this paper

@inproceedings{Khoshnevisan2002LocalTO, title={Local Times of Additive Lévy Processes}, author={Davar Khoshnevisan and Yimin Xiao and Yuquan Zhong}, year={2002} }