Hitting of a line or a half-line in the plane by two-dimensional symmetric stable Lévy processes
- Isozaki, Yasuki
Publication date
August 2011
DOI Publisher
Elsevier B.V. ISSN
0304-4149 Citation count (estimate)
2Abstract
AbstractLet (X(t),Y(t)) be a symmetric α-stable Lévy process on R2 with 1<α≤2 and LY(t) be the local time at 0 for Y(t). A multivariate asymptotic estimate is obtained involving the first hitting time and place of the positive half of the X-axis, and LY(⋅) up to then. The method is based on the fluctuation identities for two-dimensional processes and the same method is applicable for a wider class of processes.When (X(0),Y(0))=(0,1), the law of the first hitting place of the whole X-axis is shown to have the explicit density const/Ψ(1,x) where Ψ is the characteristic exponent
Add to ORKG