## Electronic Communications in Probability

### 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 $\mathbb{R}^d$. 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.

#### Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 56, 614-627.

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

https://projecteuclid.org/euclid.ecp/1465233483

Digital Object Identifier
doi:10.1214/ECP.v13-1428

Mathematical Reviews number (MathSciNet)
MR2461535

Zentralblatt MATH identifier
1189.60139

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces

Rights