Asymptotic expansions for renewal measures in the plane

Abstract

Let P be a distribution in the plane and define the renewal measure R=ΣP *n where * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47655/1/440_2004_Article_BF00348749.pd