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Multi-dimensional additively stationary random functions on convex structures
Author(s):
O.
I.
Ponomarenko;
Yu.
D.
Perun
Translated by:
V. Zayats
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 74
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 74
(2007),
133-146.
MSC (2000):
Primary 60G10;
Secondary 60G57
Posted:
July 5, 2007
Retrieve article in:
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Additional information
Abstract:
Some classes of the wide-sense additively stationary generalized random functions taking values in a complex Hilbert space are considered. These random functions are defined on certain types of convex cones and convex sets belonging to a real vector space that can be interpreted as commutative additive semigroups endowed with the identical involution  . Here, stationarity is understood as  -stationarity with respect to a semigroup in the sense of earlier papers by the authors. For the above-mentioned classes of additively stationary random functions, spectral expansions are obtained for both these functions and their correlation functions. Properties of these expansions are studied and the problem of the extension of the described additively stationary functions to wider sets in vector spaces is considered.
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Additional Information:
O.
I.
Ponomarenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, Taras Shevchenko National University, Glushkov Ave., 6, Ky{ï}v 03127, Ukraine
Yu.
D.
Perun
Affiliation:
Auditorship Department, National Bank of Ukraine, Instituts'ka Street, 9, Ky{ï}v 01601, Ukraine
Email:
perun@bank.gov.ua
DOI:
10.1090/S0094-9000-07-00703-X
PII:
S 0094-9000(07)00703-X
Keywords:
Additively stationary random function in a Hilbert space,
convex cone,
convex set,
$\alpha$-boundedness,
spectral expansion
Received by editor(s):
13/APR/2005
Posted:
July 5, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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