Moment Functions and Central Limit Theorem for Jacobi Hypergroups on [ $$0,\infty $$ [
Tóm tắt
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
$$\mathbb H $$
.
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