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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 56 open journal systems 


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.


Full text: PDF

Pages: 614-627

Published on: December 8, 2008
Bibliography
  1. R. Bass, K. Burdzy, Z.-Q. Chen and M. Hairer, Stationary distributions for diffusions with inert drift. Probab. Theory Rel. Fields (to appear)
  2. K. Bogdan, K. Burdzy and Z.-Q. Chen, Censored stable processes. Probab. Theory Related Fields 127 (2003), no. 1, 89--152. MR2006232 (2004g:60068)
  3. K. Burdzy, R. Hołyst and Ł. Pruski, Brownian motion with inert drift, but without flux: a model. Physica A 384 (2007), 278--284.
  4. K. Burdzy and D. White, A Gaussian oscillator. Electron. Comm. Probab. 9 (2004), 92--95 (electronic). MR2108855 (2005i:60173)
  5. D. White, Processes with inert drift. Electron. J. Probab. 12 (2007), no. 55, 1509--1546 (electronic). MR2365876 (2008k:60195)
















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Electronic Communications in Probability. ISSN: 1083-589X