Complete exact laws

• Autorzy: Adler, A.
• Języki publikacji: EN

Abstrakty

EN

Consider independent and identically distributed random variables {X,X_n, n ≥ 1} with xP{X > x} ~α(log x)^α, where α > −1 and P{X < −x} = o(P{X > x}). Even though the mean does not exist, we establish Laws of Large Numbers of the form [formula].. for all ε > 0 and a particular nonsummable sequence {c_n, n ≥ 1}, where L ≠ 0.

Słowa kluczowe

EN

strong law of large numbers; weak law of large numbers; complete convergence

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 1
• Strony: 215--222
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Adler, A.

• Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois, 60616, U.S.A.

Bibliografia

• [1] A. Adler, Generalized one-sided laws of the iterated logarithm for random variables barely with or without finite mean, J. Theoret. Probab. 3 (1990), pp. 587-597.
• [2] A. Adler, Exact strong laws, Bull. Inst. Math. Acad. Sinica 28 (2000).
• [3] T. C. Hu, D. Szynal and A. I. Volodin, A note on complete convergence for arrays, Statist. Probab. Lett 38 (1998), pp. 27-31.