Moment Functions and Central Limit Theorem for Jacobi Hypergroups on [ $$0,\infty $$ [

Waldemar Grundmann ()
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Waldemar Grundmann: Technische Universität Dortmund

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 278-300

Abstract: Abstract In this paper, we derive sharp estimates and asymptotic results for moment functions on Jacobi type hypergroups. Moreover, we use these estimates to prove a central limit theorem (CLT) for random walks on Jacobi hypergroups with growing parameters $$\alpha ,\beta \rightarrow \infty $$ . As a special case, we obtain a CLT for random walks on the hyperbolic spaces $${H}_d(\mathbb F )$$ with growing dimensions $$d$$ over the fields $$\mathbb F =\mathbb R ,\ \mathbb C $$ or the quaternions $$\mathbb H $$ .

Keywords: Radial random walks; Central limit theorems; Normal limits; Moment functions; Asymptotic results; Hyperbolic spaces; Jacobi hypergroups (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0465-9

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