Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries

Details Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries

2011-10-13

arxiv.org/abs/1110.3064v1

Mathematics

Probability

Scientific paper

This paper is concerned with the small time behaviour of a L\'{e}vy process $X$. In particular, we investigate the {\it stabilities} of the times, $\Tstarb(r)$ and $\Tbarb(r)$, at which $X$, started with $X_0=0$, first leaves the space-time regions $\{(t,y)\in\R^2: y\le rt^b, t\ge 0\}$ (one-sided exit), or $\{(t,y)\in\R^2: |y|\le rt^b, t\ge 0\}$ (two-sided exit), $0\le b<1$, as $r\dto 0$. 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 $L^p$. 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.

Affiliated with

Also associated with

No associations

Rating

Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries 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 Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-521540