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Convergence of sequences of iterates of random-valued vector functions

Rafał Kapica (2003)

Colloquium Mathematicae

Given a probability space (Ω,, P) and a closed subset X of a Banach lattice, we consider functions f: X × Ω → X and their iterates f : X × Ω X defined by f¹(x,ω) = f(x,ω₁), f n + 1 ( x , ω ) = f ( f ( x , ω ) , ω n + 1 ) , and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).

Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro Caputo, Paolo Dai Pra, Gustavo Posta (2009)

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

We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results...

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