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Abstrakty
A condition implying the strong law of large numbers for trajectories of a normal non-contractive operator is given. The condition has been described in terms of a spectral measure, in the spirit of the well-known theorem of V. F. Gaposhkin. To embrace the non-contractive operators we pass from the classical arithmetic (Cesáro) means to the Borel methods of summability.
Czasopismo
Rocznik
Tom
Strony
85--99
Opis fizyczny
Biblogr. 7 poz.
Twórcy
autor
- Faculty of Mathematics University of Łódź, Banacha 22, PL-90-238 Łódź,, Poland
Bibliografia
- [1] G. Alexits, Convergence Problems of Orthogonal Series, Pergamon Press, New York- Oxford-Paris 1961.
- [2] N. H. Bingham, Summability methods and dependent strong laws, Progr. Probab. Statist. 11 (Í986), pp. 291-300.
- [3] N. H. Bingham and M. Maejima, Summability methods and almost sure convergence, Z. Wahrsch. verw. Gebiete 68 (1985), pp. 383-392.
- [4] V. F. Gaposhkin, Criteria of the strong law of large numbers for some classes of stationary processes and homogeneous random fields (in Russian), Theory Probab. Appl. 22 (1977), pp. 295-319.
- [5] V. F. Gaposhkin, Individual ergodic theorem for normal operators in L2 (in Russian), Functional Anal. Appl. 15 (1981), pp. 18-22.
- [6] G. W. Hardy, Divergent Series, University Press, Oxford 1956.
- [7] L. Włodarski, Sur les méthodes continues de limitation du type de Borei, Ann. Polon. Math. IV,2 (1958), pp. 137-174.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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