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Entropy of probability kernels from the backward tail boundary

Tim Austin (2015)

Studia Mathematica

A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space (X,μ). These works have culminated in a proof by Downarowicz and Frej that various competing definitions all coincide, and that the resulting quantity is uniquely characterized by certain abstract properties. On the other hand, Makarov has shown that this 'operator...

Ergodic behaviour of “signed voter models”

G. Maillard, T. S. Mountford (2013)

Annales de l'I.H.P. Probabilités et statistiques

We answer some questions raised by Gantert, Löwe and Steif (Ann. Inst. Henri Poincaré Probab. Stat.41(2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site x and a site y is negative (respectively positive) the site y will contribute towards the flip rate of x if and only if the two current spin values are equal (respectively opposed)....

Ergodic behaviour of stochastic parabolic equations

Jan Seidler (1997)

Czechoslovak Mathematical Journal

The ergodic behaviour of homogeneous strong Feller irreducible Markov processes in Banach spaces is studied; in particular, existence and uniqueness of finite and σ -finite invariant measures are considered. The results obtained are applied to solutions of stochastic parabolic equations.

Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere

Ľubomír Baňas, Zdzisław Brzeźniak, Mikhail Neklyudov, Martin Ondreját, Andreas Prohl (2015)

Czechoslovak Mathematical Journal

We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...

Ergodicity of a certain class of non Feller models : applications to 𝐴𝑅𝐶𝐻 and Markov switching models

Jean-Gabriel Attali (2004)

ESAIM: Probability and Statistics

We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.

Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models

Jean-Gabriel Attali (2010)

ESAIM: Probability and Statistics

We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.

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