Strong laws of large numbers for random walks associated with a class of one-dimensional convolution structures

Abstract

We derive strong laws of large numbers for birth and death random walks and random walks on polynomial hypergroups for which the coefficients of the three-term-recurrence formula of the associated orthogonal polynomials satisfy limn→∞na (an-cn)=ϱ wherea∈]0, 1[ and ϱ>0. We also present these laws for random walks on Sturm-Liouville hypergroups on ℝ+ for which a corresponding asymptotic condition holds. Our paper supplements articles ofVoit [9] andZeuner [14] in which the casesa=0 anda=1 are considered.