A KINGMAN CONVOLUTION APPROACH
TO BESSEL PROCESSES
Abstract: In this paper we study Bessel processes in terms of the Kingman convolution method.
In particular, we propose a higher dimensional model of the Kingman convolution algebras.
We show that every Bessel process started at 0 is induced by a Kingman convolution.
Moreover, a new concept of increments of stochastic processes is introduced. It permits to
regard Bessel processes as “stationary and independent increments processes”.
2000 AMS Mathematics Subject Classification: Primary: 60G48, 60G51, 60G57;
Secondary: 60J25, 60J60, 60J99.
Keywords and phrases: Kingman convolution, radial characteristic function,
independent increment-type processes, Rayleigh distribution, Urbanik convolution
algebras.