Multidimensional additive stationary random functions on the convex structures. (Ukrainian, English) Zbl 1150.60015

Ponomarenko, O. I.; Perun, Yu. D.

Teor. Jmovirn. Mat. Stat. 74, 116-128 (2006); translation in Theory Probab. Math. Stat. 74, 133-146 (2007).

The authors deal with classes of additive stationary in wide sense generalized random functions with values in complex Hilbert space. These functions are defined on some types of convex cones and convex sets of real vector space. For such classes of additive stationary random functions the spectral decomposition for functions themselves and for their correlation functions are obtained. Properties of these spectral decompositions are studied.

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

60G10	Stationary stochastic processes
60G57	Random measures

Keywords:

multidimensional additive stationary random functions; convex structures; complex Hilbert space; convex cone; spectral decomposition; correlation function