We exploit the fact that the classical Bernoulli systems are con-tractive iterated function systems (IFS) of affine type to prove a number of properties of the infinite Bernoulli convolution measures ν λ. We develop and use a new duality notion for affine IFSs. This duality is based on a natural transfer operator R W , and on an associated random walk process Px. We show that the absolute-squar...

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We exploit the fact that the classical Bernoulli systems are con-tractive iterated function systems (IFS) of affine type to prove a number of properties of the infinite Bernoulli convolution measures ν λ. We develop and use a new duality notion for affine IFSs. This duality is based on a natural transfer operator R W , and on an associated random walk process Px. We show that the absolute-squar...

This paper presents a simulation study of diierent token generation policies for a leaky bucket traac shaper. In particular, the paper addresses the following question: Can the performance of a leaky bucket traac shaper be improved by matching the token generation policy to the characteristics of the input traac? Three diierent token generation policies are considered: Deterministic, Bernoulli,...

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Ber...

A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the background...

Let β > 1 be a non-integer. We consider β-expansions of the form ∑∞ i=1 di βi , where the digits (di)i≥1 are generated by means of a random map Kβ defined on {0, 1}N× [0, bβc/(β − 1)]. We show that Kβ has a unique measure νβ of maximal entropy log(1 + bβc). Under this measure, the digits (di)i≥1 form a uniform Bernoulli process, and the projection of this measure on the second coordinate is an ...

The discrete-time batch Markovian arrival process (D-BMAP) was first defined in [2]. The D-BMAP can represent a variety of arrival processes which include, as special cases, the Bernoulli arrival process, the Markov-modulated Bernoulli process (MMBP), the discrete-time Markovian arrival process (D-MAP), and their superpositions. It is the discrete-time version of the versatile Markovian point p...