A large deviation principle for polynomial hypergroups. (English) Zbl 0857.60019
Summary: Let \(S_n\), \(n\geq 1\), be a random walk on a polynomial hypergroup \((\mathbb{N}_0,*)\), that is, a Markov chain on the nonnegative integers with stationary transition probabilities \(P_{ij} = \delta_i*\mu (\{j\})\), where \(\mu\) is a fixed probability measure on \(\mathbb{N}_0\). Under certain conditions on this measure, the principle of large deviations is shown for the distributions of \(S_n/n\). This result comprises the large deviation principle for birth and death random walks associated with the polynomials generating the polynomial hypergroup.
MSC:
60F10 | Large deviations |
60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
43A62 | Harmonic analysis on hypergroups |