A law of the iterated logarithm for a class of polynomial hypergroups (Q749985)

We consider stationary \({\mathbb{N}}_ 0\)-valued Markov chains whose transition probabilities are associated with convolution structures of measures which are induced by linearization formulas of orthogonal polynomials. The best known examples are random walks on polynomial hypergroups and generalized birth and death random walks. Using central limit theorems derived in a recent paper of the author and some martingale arguments, we here prove a law of the iterated logarithm for a class of such Markov chains.