Boundary behavior for random walks in cones

Abstract

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.

37 pages, 2 figures. The previous version of this article (arXiv:1803.09253V2) has been split into two parts: the first part is the new version (arXiv:1803.09253v3) and the second will be part of a joint article with Jetlir Duraj and Vitali Wachtel (to appear soon on arXiv)