Distribution of the First Hitting Point on a Boundary Set for a Random Walk in a Lattice Strip
We consider a time-homogeneous random walk in a strip of a two-dimensional lattice whose transition probabilities are invariant under shifts along one of the coordinates. We study the limiting distribution of the first hitting point into a boundary set as the initial condition tends to infinity. Explicit expressions are obtained for this limiting distribution for negative and zero mean drift.
math.PR↗