Central limit theorems for hyperbolic spaces and Jacobi processes on [0,infinity[

作者：Voit Michael^*

来源：Monatshefte fur Mathematik, 2013, 169(3-4): 441-468.

DOI：10.1007/s00605-012-0460-3

• Laplace integral representation
• Limits of Jacobi functions
• Asymptotic results
• Spherical functions
• Hyperbolic spaces
• Radial random walks
• Central limit theorems
• Normal limits
• Rayleigh distributions

We present a unified approach to a couple of central limit theorems for the radial behavior of radial random walks on hyperbolic spaces as well as for time-homogeneous Markov chains on whose transition probabilities are defined in terms of Jacobi convolutions. The proofs of all central limit theorems are based on corresponding limit results for the associated Jacobi functions . In particular, we consider the limit , the limit for , and the behavior of the Jacobi function for small . The proofs of all these limit results are based on the known Laplace integral representation for Jacobi functions. Parts of the results are known, other improve known ones, and other are new.

• 出版日期2013-3