A limit theorem for two-dimensional random walk conditioned to stay in a cone : Michio Shimura, University of Tsukuba, Ibaraki, Japan

Abstract

Consider a two-dimensional random walk with mean $0$ and covariance $\left(\begin{array}{l}l0\\01\end{array}\right)$ . Under some additional assumptions on the random walk the limit theorem is established for the normalized random walk which is conditioned to stay in a cone for a unit of time. The conditioned limit theorem is used to prove a tail formula for the distribution of the exit time of the random walk from a cone.