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Characterization of weak limits of randomly indexed sequences

โœ Scribed by A. Krajka

Book ID
104301471
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
103 KB
Volume
50
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

Let {Xn; nยฟ1} be an arbitrary sequence of random elements deรฟned on a probability space ( ; A; P) with a nonatomic measure P and taking values in a separable complete metric space (S; ). In this paper we characterize the set of all possible weak limits of the sequences {XN n ; nยฟ1}, where {Nn; nยฟ1} is a sequence of positive integer-valued random variables. The proof shows how, for a given probability law F( ), we can deรฟne a random sequence {Nn; nยฟ1} satisfying

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## Abstract Let {__X~n~__, __n__ โฉพ 1) be a sequence of independent random variables such that __EX~n~__ = __a~n~__, __E__(__X~n~__ โˆ’ __a~n~__)^2^ = ฯƒ, __n__ โฉพ 1. Let {__N~n~, n__ โฉพ 1} be a sequence of positive integerโ€valued random variables. Let us put In this paper we present necessary and suffi