Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Infinitely Divisible Central Probability Measures on Compact Lie Groups -
 

Summary: Infinitely Divisible Central Probability
Measures on Compact Lie Groups -
Regularity, Semigroups and Transition Kernels
David Applebaum,
Department of Probability and Statistics,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
Abstract
We introduce a class of central symmetric infinitely divisible prob-
ability measures on compact Lie groups by lifting the characteristic ex-
ponent from the real line via the Casimir operator. The class includes
Gauss, Laplace and stable-type measures. We find conditions for such
a measure to have a smooth density and give examples. The Hunt
semigroup and generator of convolution semigroups of measures are
represented as pseudo-differential operators. For sufficiently regular
convolution semigroups, the transition kernel has a tractable Fourier
expansion and the density at the neutral element may be expressed as
the trace of the Hunt semigroup. We compute the short time asymp-

  

Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield

 

Collections: Mathematics