Markov processes with product-form stationary distribution
Krzysztof Burdzy, University of Washington
David White, Belmont University
Abstract
We consider a continuous time Markov process (X,L), where X jumps
between a finite number of states and L is a piecewise linear
process with state space Rd. The process L represents an
“inert drift” or “reinforcement.” We find sufficient and
necessary conditions for the process (X,L) to have a stationary
distribution of the product form, such that the marginal distribution
of L is Gaussian. We present a number of conjectures for processes
with a similar structure but with continuous state spaces.
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