Search Results

You are looking at 1 - 10 of 59 items for :

  • "central limit theorems" x
  • All content x
Clear All

everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988), 561-574. MR 89i :60045 An almost everywhere central limit theorem Math. Proc. Cambridge Philos. Soc

Restricted access

134 Bercu, B. , On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications, Stochastic Process. Appl. 111 (2004

Restricted access

Abstract  

This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central limit theorem.

Restricted access

] B rosamler , G. A. , An almost everywhere central limit theorem , Math. Proc. Camb. Phil. Soc. , 104 ( 1988 ), 561 – 574 . [4] G onchigdanzan , K

Restricted access

Abstract  

Let (X k) be a sequence of independent r.v.’s such that for some measurable functions gk : R kR a weak limit theorem of the form

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$g_k (X_1 , \ldots ,X_k )\xrightarrow{\mathcal{L}}G$$ \end{document}
holds with some distribution function G. By a general result of Berkes and Csáki (“universal ASCLT”), under mild technical conditions the strong analogue
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{1} {{D_N }}\sum\limits_{k = 1}^N {d_k I\left\{ {g_k (X_1 , \ldots ,X_k ) \leqq x} \right\} \to G(x)} a.s.$$ \end{document}
is also valid, where (d k) is a logarithmic weight sequence and D N = ∑k=1 N d k. In this paper we extend the last result for a very large class of weight sequences (d k), leading to considerably sharper results. We show that logarithmic weights, used traditionally in a.s. central limit theory, are far from optimal and the theory remains valid with averaging procedures much closer to, in some cases even identical with, ordinary averages.

Restricted access