Spectral analysis of subordinate Brownian motions in half-line

Details Spectral analysis of subordinate Brownian motions in half-line Spectral analysis of subordinate Brownian motions in half-line

2010-06-02

arxiv.org/abs/1006.0524v4

Studia Math. 206(3) (2011) 211-271

Mathematics

Probability

58 pages, 1 figure. Major revision

Scientific paper

10.4064/sm206-3-2

We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely monotone density; or, equivalently, symmetric Levy processes whose Levy measure has completely monotone density on the positive half-line. Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generalized eigenfunction expansion of the transition operators is derived. As an application, a formula for the distribution of the first passage time (or the supremum functional) is obtained.

Affiliated with

Also associated with

No associations

Rating

Spectral analysis of subordinate Brownian motions in half-line 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 Spectral analysis of subordinate Brownian motions in half-line, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral analysis of subordinate Brownian motions in half-line will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513065