Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 77, 23 pp.
Limits of sequences of Markov chains
We study the limiting object of a sequence of Markov chains analogous to the limits of graphs, hypergraphs, and other objects which have been studied. Following a suggestion of Aldous, we assign to a convergent sequence of finite Markov chains with bounded mixing times a unique limit object: an infinite Markov chain with a measurable state space. The limits of the Markov chains we consider have discrete spectra, which makes the limit theory simpler than the general graph case, and illustrates how the discrete spectrum setting (sometimes called "random-free" or "product measurable") is simpler than the general case.
Electron. J. Probab., Volume 20 (2015), paper no. 77, 23 pp.
Accepted: 20 July 2015
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 03C20: Ultraproducts and related constructions
This work is licensed under aCreative Commons Attribution 3.0 License.
Towsner, Henry. Limits of sequences of Markov chains. Electron. J. Probab. 20 (2015), paper no. 77, 23 pp. doi:10.1214/EJP.v20-4188. https://projecteuclid.org/euclid.ejp/1465067183