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Almost Sure Convergence for Stochastic Integrals
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Almost Sure Convergence in Extreme Value Theory
Mathematische Nachrichten, 1998AbstractLet X1, …, Xn be independent random variables with common distribution function F. Define equation image and let G(x) be one of the extreme‐value distributions. Assume F ∈ D(G), i.e., there exist an> 0 and bn ∈ ℝ such that equation image .Let l(−∞,x)(·) denote the indicator function of the set (−∞,x) and S(G) =: {x : 0 < G(x) < 1 ...
Cheng, Shihong +2 more
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Almost sure convergence of random gossip algorithms
2007 46th IEEE Conference on Decision and Control, 2007In this paper we provide a proof of almost sure convergence to consensus for an extremely general class of edge selection processes. The proof also applies to continuous time gossip algorithms.
PICCI, GIORGIO, TAYLOR T. J.
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Summability methods and almost sure convergence
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1985The authors investigate almost sure convergence for sequences of i.i.d. random variables under different methods of summability. We say \(s_ n\to s\) (P), if \(\sum^{\infty}_{j=0}s_ jP(S_ n=j)\to s\) as \(n\to \infty\), where \(S_ n:=\xi_ 1+...+\xi_ n\), and \(\xi_ 1,\xi_ 2,..\). are integer-valued independent random variables.
Bingham, N. H., Maejima, Makoto
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