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.
@article{bwmeta1.element.doi-10_2478_v10062-008-0016-0, author = {Anna Walczuk}, title = {Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric}, journal = {Annales UMCS, Mathematica}, volume = {62}, year = {2008}, pages = {149-159}, zbl = {1184.60028}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0016-0} }
Anna Walczuk. Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric. Annales UMCS, Mathematica, Tome 62 (2008) pp. 149-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0016-0/
Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968. | Zbl 0172.21201
Dudley, R. M., Real Analysis and Probability, Wadsworth Inc., Belmont, 1989. | Zbl 0686.60001
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. | Zbl 0486.60023
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. | Zbl 0588.60058
Meyn, S. P., Tweedie, R. L., Computable bounds for geometric convergence rates of Markov chains, Ann. Appl. Probab. 4 (1994), 981-1011. | Zbl 0812.60059
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. | Zbl 1029.60084
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. | Zbl 0936.60037