Displaying similar documents to “Lévy classes and self-normalization.”

Ordered random walks.

Eichelsbacher, Peter, König, Wolfgang (2008)

Electronic Journal of Probability [electronic only]

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Necessary and sufficient conditions for weak convergence of random sums of independent random variables

Andrzej Krajka, Zdzisław Rychlik (1993)

Commentationes Mathematicae Universitatis Carolinae

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Let { X n , n ≥ 1 } be a sequence of independent random variables such that E X n = a n , E ( X n - a n ) 2 = σ n 2 , n ≥ 1 . Let { N n , n ≥ 1 } be a sequence od positive integer-valued random variables. Let us put S N n = ∑ k = 1 N n X k , L n = ∑ k = 1 n a k , s n 2 = ∑ k = 1 n σ k 2 , n ≥ 1 . In this paper we present necessary and sufficient conditions for weak convergence of the sequence { ( S N n - L n ) / s n , n ≥ 1 } , as n → ∞ . The obtained theorems extend the main result of M. Finkelstein and H.G. Tucker (1989).