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Journal of the London Mathematical Society 1996 53(1):197-208; doi:10.1112/jlms/53.1.197
© 1996 by London Mathematical Society
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© The London Mathematical Society

A Large Deviation Principle for Polynomial Hypergroups

Martin Ehring

GSF-München, MEDIS-Institut Postfach 1129, 85758 Oberschleissheim, Germany

Received 14 March 1994. Revision received 24 August 1994.

Let Sn, n ≥ 1, be a random walk on a polynomial hypergroup (N0, *), that is, a Markov chain on the nonnegative integers with stationary transition probabilities Pij = {delta}i* µ({j}), where µ is a fixed probability measureon N0. Under certain conditions on this measure, the principle of large deviations is shown for the distributions of Sn/n. This result comprises the large deviation principle for birth and death random walks associated with the polynomials generating the polynomial hypergroup.


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