Markov processes and exponential families
type: Item
instance of: scholarly article
title: Markov processes and exponential families
zbMATH Open document ID: 0765.60074
DOI: 10.1016/0304-4149(92)90121-6
author: Bernard Ycart
published in: Stochastic Processes and their Applications
publication date: 1993-01-16T00:00:00Z
review text: An exponential one-parameter family of distributions on a locally compact topological space \(E\) is considered. We consider also, canonically associated with it, the exponential family of distributions on \(R\). A notion of a stable Markov generator for the given exponential family on \(E\) is introduced. It is shown that under certain conditions the generator on \(E\) may be canonically associated with the generator on \(R\) with the same stability property. These results allow us to construct, both in \(E\) and \(R\), many examples of Markov processes with distributions known exactly at any given instant. Some examples of such constructions are given.
reviewed by: Piotr Staniewski
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 90071
zbMATH Keywords: Markov processes
zbMATH Keywords: exponential one-parameter family of distributions
zbMATH Keywords: stable Markov generator
zbMATH Keywords: stability property
MaRDI profile type: Publication
full work available at URL: 0304-4149(92)90121-6
OpenAlex ID: W2068823030
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description: scientific article; zbMATH DE number 90071