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On iterates of strong Feller operators on ordered phase spaces

Wojciech Bartoszek (2004)

Colloquium Mathematicae

Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities P ( x , · ) x X are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities...

On limiting towards the boundaries of exponential families

František Matúš (2015)

Kybernetika

This work studies the standard exponential families of probability measures on Euclidean spaces that have finite supports. In such a family parameterized by means, the mean is supposed to move along a segment inside the convex support towards an endpoint on the boundary of the support. Limit behavior of several quantities related to the exponential family is described explicitly. In particular, the variance functions and information divergences are studied around the boundary.

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