On extensions of Rényi conditional probability spaces
Relative generators for the action of a countable abelian group on a Lebesgue space
Symbolic computing in probabilistic and stochastic analysis
The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any...
Generators of perfect σ-algebras of -actions
Remarks on -spaces
An axiomatic definition of the entropy of a -action on a Lebesgue space
Convolution, product and Fourier transform of distributions
On regular generator of Z²-actions in exhaustive partitions
On the Rényi theory of conditional probabilities
A representation theorem for perfect partitions of -actions with finite entropy
Some properties of coalescent automorphisms of a Lebesgue space
The article contains no abstract
On abelian groups of transformations with completely positive entropy
The article contains no abstract
On the Urysohn condition and the convergence of probability distributions
Test de décrochement des distributions
A note on the convolution and the product and .
Distributional solutions in information theory, II
Spectrum of multidimensional dynamical systems with positive entropy
Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov -action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to -actions. Next, using its relative version, we extend to -actions some other general results connecting spectrum and entropy.
Relatively perfect σ-algebras for flows
We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.
On the directional entropy for ℤ²-actions on a Lebesgue space
We define the concept of directional entropy for arbitrary -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.
On extremal and perfect σ-algebras for flows
It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.
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