Title: Stationary Markov processes related to stable Ornstein--Uhlenbeck processes and the additive coalescent
Authors: Steven N. Evans and Jim Pitman
Date: July, 1997 (revised May 1998)
Abstract: We consider some classes of stationary, 
counting--measure--valued Markov processes
and their companions under time--reversal.  Examples arise
in the L\'evy--It\^o decomposition of stable Ornstein--Uhlenbeck
processes, the large--time asymptotics of the
standard additive coalescent,
and extreme value theory.  These processes share the common feature
that points in the support of the evolving counting--measure
are born or die randomly, but each point follows
a deterministic flow during its life--time.