Curve crossing for random walks reflected at their maximum

Details Curve crossing for random walks reflected at their maximum Curve crossing for random walks reflected at their maximum

2007-08-13

arxiv.org/abs/0708.1676v1

Annals of Probability 2007, Vol. 35, No. 4, 1351-1373

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000953 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000953

Let $R_n=\max_{0\leq j\leq n}S_j-S_n$ be a random walk $S_n$ reflected in its maximum. Except in the trivial case when $P(X\ge0)=1$, $R_n$ will pass over a horizontal boundary of any height in a finite time, with probability 1. We extend this by giving necessary and sufficient conditions for finiteness of passage times of $R_n$ above certain curved (power law) boundaries, as well. The intuition that a degree of heaviness of the negative tail of the distribution of the increments of $S_n$ is necessary for passage of $R_n$ above a high level is correct in most, but not all, cases, as we show. Conditions are also given for the finiteness of the expected passage time of $R_n$ above linear and square root boundaries.

Affiliated with

Also associated with

No associations

Rating

Curve crossing for random walks reflected at their maximum 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 Curve crossing for random walks reflected at their maximum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curve crossing for random walks reflected at their maximum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23316