Title: Stick-breaking processes, clumping, and Markov chain occupation laws,
Abstract: We consider the connections among `clumped' residual allocation models
(RAMs), a general class of stick-breaking processes including Dirichlet
processes, and the occupation laws of certain discrete space time-inhomogeneous
Markov chains related to simulated annealing and other applications. An
intermediate structure is introduced in a given RAM, where proportions between
successive indices in a list are added or clumped together to form another RAM.
In particular, when the initial RAM is a Griffiths-Engen-McCloskey (GEM)
sequence and the indices are given by the random times that an auxiliary Markov
chain jumps away from its current state, the joint law of the intermediate RAM
and the locations visited in the sojourns is given in terms of a `disordered'
GEM sequence, and an induced Markov chain. Through this joint law, we identify
a large class of `stick breaking' processes as the limits of empirical
occupation measures for associated time-inhomogeneous Markov chains.