Displaying similar documents to “An example of a weak Bernoulli process which is not finitary”

A family of stationary processes with infinite memory having the same p-marginals. Ergodic and spectral properties

M. Courbage, D. Hamdan (2001)

Colloquium Mathematicae

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We construct a large family of ergodic non-Markovian processes with infinite memory having the same p-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman-Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.

Stochastic differential equation driven by a pure-birth process

Marta Tyran-Kamińska (2002)

Annales Polonici Mathematici

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A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.

Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud (2010)

ESAIM: Probability and Statistics

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In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

Systems of differential equations modeling non-Markov processes

Irada Dzhalladova, Miroslava Růžičková (2023)

Archivum Mathematicum

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The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.

On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains

Ion Grama, Émile Le Page, Marc Peigné (2014)

Colloquium Mathematicae

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We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed...