The strong law of large numbers for weighted averages under dependence assumptions | Zendy

Tapas K. Chandra | Zendy; Subhashis Ghosal | Zendy

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The strong law of large numbers for weighted averages under dependence assumptions

Author(s) -

Tapas K. Chandra,

Subhashis Ghosal

Publication year - 1996

Publication title -

journal of theoretical probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.671

H-Index - 42

eISSN - 1572-9230

pISSN - 0894-9840

DOI - 10.1007/bf02214087

Subject(s) - independent and identically distributed random variables , mathematics , law of large numbers , random variable , set (abstract data type) , combinatorics , statistics , computer science , programming language

Strong laws of large numbers (SLLN) for weighted averages are proved under various dependence assumptions when the variables are not necessarily independent or identically distributed. The results considerably extend the existing results. Weighted versions of the Marcinkiewicz-Zygmund SLLN are also formulated and proved under a similar set up. It seems that such results are not known even for independent and identically distributed random variables.

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