A random walk on Z with drift driven by its occupation time at zero

Details A random walk on Z with drift driven by its occupation time at zero A random walk on Z with drift driven by its occupation time at zero

2007-11-30

arxiv.org/abs/0711.4871v1

Mathematics

Probability

Scientific paper

We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes according to the rate of decay of the drift. In particular, when the rate is sufficiently slow, the position of the random walk, properly normalized, converges to a symmetric exponential law. In this regime, in contrast to the classical case, the range of the walk scales differently from its position.

Affiliated with

Also associated with

No associations

Rating

A random walk on Z with drift driven by its occupation time at zero 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 A random walk on Z with drift driven by its occupation time at zero, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A random walk on Z with drift driven by its occupation time at zero will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-702495