Results 271 to 280 of about 11,838 (304)

On almost sure convergence of adaptive algorithms

IEEE Transactions on Automatic Control, 1986
We present an extension of the Furstenberg-Kesten theorem on the convergence of random matrices. This extension is applied to the study of almost sure convergence of certain adaptive algorithms. In particular, we establish that the NLMS algorithm is almost surely convergent under extremely weak necessary and sufficient conditions.
D. Shi, F. Kozin
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Almost sure convergence of sample range

Extremes, 2007
An almost sure limit theorem is derived for the sample range statistics \( R_n=\max_{1\leq i\leq n} X_i-\min_{1\leq i\leq n} X_i \), where \(X_i\) are i.i.d. r.v.s. It states that if for some nonrandom \(\alpha_n\), \(\beta_n\) and some nondegenerate CDF \(G\) \(\zeta_n=\alpha_n(R_n-\beta_n)\) converges in distribution to \(G\) then at any point \(x ...
Zhongquan, Tan, Zuoxiang, Peng, Nadarajah, Saralees   +2 more
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On almost sure convergence of asymptotic martingales

1993
Summary: The aim of this paper is to give a characterization of almost sure convergence for sequences of random variables, which do not necessarily have first moments. An example of such characterization was given by \textit{I. A. Dzhvarsheishvili} [Theory Probab. Appl. 33, 260-269 (1988)], where a notion of a \(D_v\)-amart was introduced. We show that
Kruk, Łukasz, Zięba, Wiesław (1950- )
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Epi-convergence almost surely, in probability and in distribution

Annals of Operations Research, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the almost sure convergence of Syracuse sequences

Statistics & Probability Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Slakmon, Alain, Macot, Luc
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Almost sure convergence of the Hill estimator

Mathematical Proceedings of the Cambridge Philosophical Society, 1988
AbstractIn this note we characterize those sequencesknsuch that the Hill estimator of the tail index based on theknupper order statistics of a sample of sizenfrom a Pareto-type distribution is strongly consistent.
Deheuvels, Paul, Haeusler, Erich, Mason, David M.   +2 more
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Regularity and almost sure convergence

1995
Summary: We give a sufficient condition for almost sure convergence in the sense of \textit{E. Hensz} and \textit{R. Jajte} [Math. Z. 193, 413-429 (1986; Zbl 0613.46056)] to be equivalent to almost uniform convergence.
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Almost Sure Convergence of Renewal Processes

2018
Consider some renewal sequence, that is, a sequence of partial sums {Sn}n≥0 of independent identically distributed random variables {Xn}n≥1. Our aim in this chapter is to show that various functionals of partial sums and corresponding renewal processes are asymptotically equivalent if one considers them from the point of view of generalized renewal ...
Valeriĭ V. Buldygin, Karl-Heinz Indlekofer, Oleg I. Klesov, Josef G. Steinebach   +3 more
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Almost Sure Convergence.

Journal of the American Statistical Association, 1975
M. H. D., William F. Stout
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Almost sure convergence and bounded entropy

Israel Journal of Mathematics, 1988
Let (\({\mathcal X},\mu)\) be a probability space, \(S_ n\) a sequence of operators on \(L^ 2(\mu)\), \(\| S_ n\| \leq 1\), \(T_ j\) a sequence of positive isometric operators satisfying \(T_ j(1)=1\), \(J^{-1}\sum_{j\leq J}T_ jf\to \int f d\mu\) \(\forall f\in L^ 1\) and \(T_ jS_ n=S_ nT_ j\).
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