We introduce an invariant of cohomology in Bernoulli shifts, which is used to answer a question about cohomology of Hölder functions with finitary functions whose coding time is integrable. When restricted to the class of Hölder functions, this invariant even provides a criterion of cohomology.
The author in the paper evaluates the Rényi distances between two Gaussian measures using properties of nuclear operators and expresses the formula for the asymptotic rate of the Rényi distances of stationary Gaussian measures by the corresponding spectral density functions in a general case.
A method is shown for the simulation in Rn of second order stationary random functions with given isotropic covariance. Particular solutions, ilustrated with examples, are provided in R1, R2 and R3.
We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.
In the limit theory for strictly stationary processes , the decomposition proved to be very useful; here is a bimeasurable and measure preserving transformation an is a martingale difference sequence. We shall study the uniqueness of the decomposition when the filtration of is fixed. The case when the filtration varies is solved in [13]. The necessary and sufficient condition of the existence of the decomposition were given in [12] (for earlier and weaker versions of the results see [7])....