Right inverses of Levy processes: the excursion measure in the general case

Details Right inverses of Levy processes: the excursion measure in the general case Right inverses of Levy processes: the excursion measure in the general case

2010-03-10

arxiv.org/abs/1003.2122v1

Mathematics

Probability

12 pages

Scientific paper

This article is about right inverses of Levy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.

Affiliated with

Also associated with

No associations

Rating

Right inverses of Levy processes: the excursion measure in the general case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Right inverses of Levy processes: the excursion measure in the general case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Right inverses of Levy processes: the excursion measure in the general case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-342129