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The Tandori theorem concerning the sufficient condition for the unconditional a.e. convergence of orthogonal series is generalized for the bundle convergence in La-space over a cr-fdte von Neumann ...
Let (5,J be a sequence of random vectors with values in a Banach space X with distributions pen weakly converging to a given distribution p. We characterize a general form of a distribution of a we...
Let XI, X,, . .. be i.i.d. random variables with a commondf. P.LetS,=X,+ ...+ X,,n>1,andMm=max,s,Xk,n21. In this paper for a large class of subexponential distributions we estimate the rate of conv...
In this paper, we shall be concerned with weak convergence of the randomly indexed versions of the standard and 'Fndependence" empirical processes, in the general framework of stochastic processes ...
In this paper we propose a generalised iterative algorithm for calcu- lating variational Bayesian estimates for a normal mixture model and investigate its convergence properties. It is shown theoret...
As the distribulivn function (dd) of the suitably normalized general intermediate (or central) term of order statistics converges on an interval [c, dl to an arbitrary nondecreasing function, the c...
Let X,, n 2 1, be a sequence of independent and identically distributed rmdom variables and X,,, < X,,, < . . . < X,, denote the order statistics of Xi,.. ., X,. For any sequenoe 01 integers {k,) w...
We prove almost sure versions of distributional limit theorems for central order statistics. We develop a new method which not only gives a simplified proof of existing results in the literature, bu...
In this paper we present new suficient conditions for complete convergence for $urns of arrays of rowwise independent random variables. These conditions appear to be necessary and sufficient in the...
Statistical version of the central limit theorem (CLT) with random matrix normalization is established for random fields with valuea in a space Rk (k 3 1). Dependence structure of the field under c...
In this paper we present functional random-sum central limit theorems with almost sure convergence for independent nonidentically distributed random variables. We consider the case where the summat...
We apply the theory of finite difference equations to the central limit theorem, using interpolation of Banach spaces and Fourier multipliers. Let S,T be a normalized sum of i.i.d. random vectors, ...
In this note, we are interested in the regularity in the sense of total variation of the joint laws of multiple stable stochastic integrals. Namely, we show that the convergence L 􀀀 Id1 ...
A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact.
We derive the l∞ convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the Gram matrix of the design and...

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