Individual ergotic theorem for non-contractive normal operators

• Autorzy: Jajte R.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

strong law of large numbers; individual ergodic theorem; normal operator; spectral measure; (non-)contractivity; Borel methods of summability; Mittag-Leffler’s function; almost sure convergence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 1
• Strony: 85--99
• Opis fizyczny: Biblogr. 7 poz.

Twórcy

autor

Jajte R.

• 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.