Markov processes and exponential families
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.
exponential one-parameter family of distributions
scientific article; zbMATH DE number 90071