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

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 $ .