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2008 Markov processes with product-form stationary distribution
Krzysztof Burdzy, David White
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Electron. Commun. Probab. 13: 614-627 (2008). DOI: 10.1214/ECP.v13-1428


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 $\mathbb{R}^d$. 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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Krzysztof Burdzy. David White. "Markov processes with product-form stationary distribution." Electron. Commun. Probab. 13 614 - 627, 2008.


Accepted: 8 December 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60139
MathSciNet: MR2461535
Digital Object Identifier: 10.1214/ECP.v13-1428

Primary: 60J25

Keywords: Inert drift , Markov process , stationary distribution

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