Complete convergence under special hypotheses

• Autorzy: Stoica G.
• Języki publikacji: EN

Abstrakty

EN

We prove Baum-Katz type theorems along subsequences of random variables under Komlós-Saks and Mazur-Orlicz type boundedness hypotheses.

Słowa kluczowe

EN

complete convergence; boundedness hypotheses; law of large numbers

PL

prawo wielkich liczb; ograniczoność; zbieżność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2012
• Tom: Vol. 35
• Strony: 91--95
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Stoica G.

• Department of Mathematical Sciences, University of New Brunswick, Saint John NB, Canada

Bibliografia

• [1] J.K. Brooks, R.V. Chacon, Continuity and compactness of measures, Adv. Math. 37 (1980) 16-26.
• [2] C. Castaing, M. Saadoune, Komlós type convergence for random variables and random sets with applications to minimization problems, Adv. Math. Econ. 10 (2007) 1-29.
• [3] S.J. Dilworth, Convergence of series of scalar- and vector-valued random variables and a subsequence priniciple in L2, Trans. Amer. Math. Soc. 301 (1987) 375-384.
• [4] E. Lesigne, D. Volný, Large deviations for martingales, Stoch. Proc. Appl. 96 (2001) 143-159.
• [5] G. Stoica, The Baum-Katz theorem for bounded subsequences, Stat. Prob. Lett. 78 (2008), 924-926.
• [6] H. von Weizsäcker, Can one drop the L1-boundedness in Komlós' subsequence theorem? Amer. Math. Monthly 111 (2004) 900-903.