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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 29, Fasc. 1,
pages 119 - 134
 

A KINGMAN CONVOLUTION APPROACH

TO BESSEL PROCESSES

Nguyen Van Thu

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.

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