One sided strong laws for random variables with infinite mean

• Autorzy: André Adler
• Języki publikacji: EN

Abstrakty

EN

This paper establishes conditions that secure the almost sure upper and lower bounds for a particular normalized weighted sum of independent nonnegative random variables. These random variables do not possess a finite first moment so these results are not typical. These mild conditions allow us to show that the almost sure upper limit is infinity while the almost sure lower bound is one.

Słowa kluczowe

EN

Almost sure convergence; Weak law of large numbers; One sided strong laws; Slow variation

Kategorie tematyczne

• 60F15: Strong theorems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 828-832

Daty

wydano

2017-01-01

otrzymano

2016-12-12

zaakceptowano

2017-05-16

online

2017-06-22

Twórcy

autor

André Adler

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Identyfikatory

DOI

10.1515/math-2017-0070