Martin boundary of random walks on certain \(d\)-dimensional hypergroups (Q1608732)

The author gives integral representation formulae for the harmonic functions of Markov chains on \(\mathbb{N}^d\) and \(\mathbb{R}^d_+\), whose transition kernels are invariant under the translation of a given product hypergroup; for \(\mathbb{N}^d\), a product of polynomial hypergroups, and for \(\mathbb{R}^d_+\) a product of Sturm-Liouville hypergroups. The main tool in deriving the representations is Choquet's theorem. In both cases, it is also shown that the only bounded harmonic functions are the constants.