# Martin boundary of a reflected random walk on a half-space

Mathematics – Probability

Scientific paper

[ 0.00 ] – not rated yet Voters 0   Comments 0

## Details Martin boundary of a reflected random walk on a half-space Martin boundary of a reflected random walk on a half-space

42 pages, preprint, CNRS UMR 8088

Scientific paper

The complete representation of the Martin compactification for reflected random walks on a half-space $\Z^d\times\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\Z^d$ : convergence of a sequence of points $z_n\in\Z^{d-1}\times\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method combined with the ratio limit theorem. The existence of non-radial limits is related to non-linear optimal large deviation trajectories.

No associations

LandOfFree

## Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

## Rating

Martin boundary of a reflected random walk on a half-space 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 Martin boundary of a reflected random walk on a half-space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Martin boundary of a reflected random walk on a half-space will most certainly appreciate the feedback.

Profile ID: LFWR-SCP-O-489698

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.