Stochastic processes indexed by Urbanik convolution algebras (Q2566570)

The paper presents a study of a class of stochastic processes which are indexed by Urbanik convolution algebras. In the first section, some definitions of Urbanik convolutions are recalled. Some examples, as generalized convolution, symmetric convolution and Kingman convolution, illustrate the given notions. Also, the notion of second-order stochastic process correlated by a given regular Urbanik convolution is given. The second section is devoted to the main result, the spectral representation of a stochastic process indexed by Urbanik convolution algebras. The paper concludes with three examples of such processes.