Title
Small and Large Time Stability of the Time Taken for a Lévy Process to Cross Curved Boundaries
Document Type
Article
Date
10-13-2011
Disciplines
Mathematics
Description/Abstract
This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and Tb*(r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) ∈ R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r -> 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in Lp. In many instances these are seen to be equivalent to relative stability of the process X itself. The analogous large time problem is also discussed.
Recommended Citation
Griffin, Philip S. and Maller, Ross A., "Small and Large Time Stability of the Time Taken for a Lévy Process to Cross Curved Boundaries" (2011). Mathematics - All Scholarship. 102.
https://surface.syr.edu/mat/102
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This is a manuscript from arXiv.org, for more information see http://arxiv.org/abs/1110.3064