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

Bálint Tóth (University of Bristol and TU Budapest)

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.

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Pages: 1-4

Publication Date: February 17, 2013

DOI: 10.1214/ECP.v18-2366

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. MR0834478
  • 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 MR2952852
  • Maxwell, Michael; Woodroofe, Michael. Central limit theorems for additive functionals of Markov chains. Ann. Probab. 28 (2000), no. 2, 713--724. MR1782272
  • Tóth, Bálint. Persistent random walks in random environment. Probab. Theory Relat. Fields 71 (1986), no. 4, 615--625. MR0833271
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