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Displaying similar documents to “Asymptotic distributions and Berry-Esseen bounds for sums of record values.”

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).

Some properties of the jacobian sn z function.

István Fenyö (1985)

Stochastica

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Using some results of the theory of functional equations we deduce some properties of the Jacobian sn z function which seem to be new. Some functional equations have also been found which are fulfilled by the sn z function which the author did not find in the literature.