کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156958 | 958901 | 2009 | 21 صفحه PDF | دانلود رایگان |
We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type π(dx)=eγxν(ex−1)dx, where νν is the density of the stable Lévy measure and γγ is a positive parameter which depends on its characteristics. These processes were introduced in [M. E. Caballero, L. Chaumont, Conditioned stable Lévy processes and the Lamperti representation, J. Appl. Probab. 43 (2006) 967–983] as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processes. In this paper, we compute explicitly the law of these Lévy processes at their first exit time from a finite or semi-finite interval, the law of their exponential functional and the first hitting time probability of a pair of points.
Journal: Stochastic Processes and their Applications - Volume 119, Issue 3, March 2009, Pages 980–1000