Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric

Anna Walczuk

Annales UMCS, Mathematica (2008)

  • Volume: 62, Issue: 1, page 149-159
  • ISSN: 2083-7402

Abstract

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We study the question of the law of large numbers and central limit theorem for an additive functional of a Markov processes taking values in a Polish space that has Feller property under the assumption that the process is asymptotically contractive in the Wasserstein metric.

How to cite

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Anna Walczuk. "Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric." Annales UMCS, Mathematica 62.1 (2008): 149-159. <http://eudml.org/doc/267569>.

@article{AnnaWalczuk2008,
abstract = {We study the question of the law of large numbers and central limit theorem for an additive functional of a Markov processes taking values in a Polish space that has Feller property under the assumption that the process is asymptotically contractive in the Wasserstein metric.},
author = {Anna Walczuk},
journal = {Annales UMCS, Mathematica},
keywords = {Markov process; invariant measure; central limit theorem; control limit theorem},
language = {eng},
number = {1},
pages = {149-159},
title = {Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric},
url = {http://eudml.org/doc/267569},
volume = {62},
year = {2008},
}

TY - JOUR
AU - Anna Walczuk
TI - Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 149
EP - 159
AB - We study the question of the law of large numbers and central limit theorem for an additive functional of a Markov processes taking values in a Polish space that has Feller property under the assumption that the process is asymptotically contractive in the Wasserstein metric.
LA - eng
KW - Markov process; invariant measure; central limit theorem; control limit theorem
UR - http://eudml.org/doc/267569
ER -

References

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  2. Dudley, R. M., Real Analysis and Probability, Wadsworth Inc., Belmont, 1989. Zbl0686.60001
  3. Dunford, N., Schwartz, J. T., Linear Operators, Interscience Publishers, Inc., New York, 1958. 
  4. Ethier, S., Kurtz, T., Markov Processes, Wiley & Sons, New York, 1986. 
  5. Helland, I. S., Central limit theorems for martingales with discrete or continuous time, Scand. J. Statist. 9 (1982), 79-94. Zbl0486.60023
  6. Kipnis, C., Varadhan, S. R. S., Central limit theorem for additive functionals of reversible Markov process and applications to simple exclusions, Comm. Math. Phys. 104 (1986), 1-19. Zbl0588.60058
  7. Meyn, S. P., Tweedie, R. L., Computable bounds for geometric convergence rates of Markov chains, Ann. Appl. Probab. 4 (1994), 981-1011. Zbl0812.60059
  8. Sethuraman, S., Varadhan, S. R. S. and Yau, H. T., Diffusive limit of a tagged particle in asymmetric exclusion process, Comm. Pure Appl. Math. 53 (2000), 972-1006. Zbl1029.60084
  9. Wu, L., Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes, Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), 121-141. Zbl0936.60037

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