Since the 1930’s many authors have studied the distribution νλ of the random series Yλ = ∑±λn where the signs are chosen independently with probability (1/2, 1/2) and 0 < λ < 1. Solomyak recently proved that for almost every λ ∈ [ 1 2 , 1], the distribution νλ is absolutely continuous with respect to Lebesgue measure. In this paper we prove that νλ is even equivalent to Lebesgue measure for alm...

The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the residual allocation model or stick-breaking. We give an overview of the limit theorems concerning the number of boxes occupied by some balls out of the first n balls thrown, and present some new re...

We give a characterization of the family of all probability measures on the extended line (−∞,+∞], which may be obtained as the distribution of the maximum of some linear Bernoulli process. On a probability space (Ω,P) consider a linear process

Consider a given pattern H and a random text T of length n. We assume that symbols in the text occur independently, and various symbols have diierent probabilities of occurrence (i.e., the so called asymmetric Bernoulli model). We are concerned with the probability of exactly r occurrences of H in the text T. We derive the generating function of this probability, and show that asymptotically it...

Let L (u, a), oo < u < + oo denote the Fourier-Stieltjes transform, 00 f eluoda(x), of a distribution function u(x), oo < x < + co . Thus if 00 /3(x) is the distribution function which is 0, J, 1 according as x -1 < x ,< 1, 1 < x, then L (u,,8) = cos u ; and so, if b is a positive constant, cos (u/b) is the transform of the distribution function /3(bx) . Hence, if a is a positive constant, the ...

A The chaos hierarchy 12 A.1 Ergodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.3 K Systems (Kolmogorov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 A.4 B-Systems (Bernoulli) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is deriv...

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is ad...

We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F. Przytycki and M. Urbański [23]. We extend their results to the overlapping region and also consider some extensions and generalizations.