Hitting distributions of alpha-stable processes via path censoring and self-similarity

Details Hitting distributions of alpha-stable processes via path censoring and self-similarity Hitting distributions of alpha-stable processes via path censoring and self-similarity

2011-12-15

arxiv.org/abs/1112.3690v1

Mathematics

Probability

Scientific paper

In this paper we return to the problem of Blumenthal-Getoor-Ray, published in 1961, which gave the law of the position of first entry of a symmetric alpha-stable process into the unit ball. Specifically, we are interested in establishing the same law, but now for a one dimensional alpha-stable process which enjoys two-sided jumps, and which is not necessarily symmetric. Our method is modern in the sense that we appeal to the relationship between alpha-stable processes and certain positive self-similar Markov processes. However there are two notable additional innovations. First, we make use of a type of path censoring. Second, we are able to describe in explicit analytical detail a non-trivial Wiener-Hopf factorisation of an auxiliary Levy process from which the desired solution can be sourced. Moreover, as a consequence of this approach, we are able to deliver a number of additional, related identities in explicit form for alpha-stable processes.

Affiliated with

Also associated with

No associations

Rating

Hitting distributions of alpha-stable processes via path censoring and self-similarity 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 Hitting distributions of alpha-stable processes via path censoring and self-similarity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hitting distributions of alpha-stable processes via path censoring and self-similarity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-136278