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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.

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