Markov processes with product-form stationary distribution

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. © 2008 Applied Probability Trust.