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

• Autorzy: Anna Walczuk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Markov process; invariant measure; central limit theorem

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2008
• Tom: 62
• Numer: 1
• Strony: 149-159

Daty

wydano

2008-01-01

online

2009-02-09

Twórcy

autor

Anna Walczuk

• Institute of Mathematics, M. Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland

Bibliografia

• Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968.
• Dudley, R. M., Real Analysis and Probability, Wadsworth Inc., Belmont, 1989.
• Dunford, N., Schwartz, J. T., Linear Operators, Interscience Publishers, Inc., New York, 1958.
• Ethier, S., Kurtz, T., Markov Processes, Wiley & Sons, New York, 1986.
• Helland, I. S., Central limit theorems for martingales with discrete or continuous time, Scand. J. Statist. 9 (1982), 79-94.
• 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.
• Meyn, S. P., Tweedie, R. L., Computable bounds for geometric convergence rates of Markov chains, Ann. Appl. Probab. 4 (1994), 981-1011.
• 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.
• 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.

Identyfikatory

DOI

10.2478/v10062-008-0016-0