Electronic Communications in Probability

Comment on a theorem of M. Maxwell and M. Woodroofe

Bálint Tóth

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Abstract

We present a direct derivation of the theorem of M. Maxwell and M. Woodroofe (Ann. Probab. vol. 28 (2000) 713-724), on martingale approximation of additive functionals of stationary Markov processes, from the non-reversible version of the Kipnis-Varadhan theorem.

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 13, 4 pp.

Dates
Accepted: 17 February 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315552

Digital Object Identifier
doi:10.1214/ECP.v18-2366

Mathematical Reviews number (MathSciNet)
MR3033596

Zentralblatt MATH identifier
1308.60027

Keywords
CLT Markov process martingale approximation

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Tóth, Bálint. Comment on a theorem of M. Maxwell and M. Woodroofe. Electron. Commun. Probab. 18 (2013), paper no. 13, 4 pp. doi:10.1214/ECP.v18-2366. https://projecteuclid.org/euclid.ecp/1465315552


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References

  • Kipnis, C.; Varadhan, S. R. S. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104 (1986), no. 1, 1–19.
  • Komorowski, Tomasz; Landim, Claudio; Olla, Stefano. Fluctuations in Markov processes. Time symmetry and martingale approximation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 345. Springer, Heidelberg, 2012. xviii+491 pp. ISBN: 978-3-642-29879-0
  • Maxwell, Michael; Woodroofe, Michael. Central limit theorems for additive functionals of Markov chains. Ann. Probab. 28 (2000), no. 2, 713–724.
  • Tóth, Bálint. Persistent random walks in random environment. Probab. Theory Relat. Fields 71 (1986), no. 4, 615–625.