Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes

 Access to full text

 Full (PDF)

1. [De] A. Dembo, Moderate deviations for martingales with bounded jumps, Elect. Comm. in Proba., Vol. 1, 1996, pp. 11-17. Zbl0854.60027MR1386290
2. [DS] J.D. Deuschel and D.W. Stroock, Large deviations, Pure and Appl. Math., Vol. 137, 1989, Academic Press. Zbl0705.60029MR997938
3. [G] S. Goldstein, Anti-symmetric functionals of reversible Markov processes, Annales d'Inst. H. Poincaré probabilités, Vol. 31, 1 (in Memoriam C. Kipnis), 1995, pp. 177-190. Zbl0813.60023MR1340036
4. [HH] P. Hall and C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, 1980. Zbl0462.60045MR624435
5. [Ka] T. Kato, Perturbation Theory For Linear Operators, 2nd ed. (2nd corrected printing), Springer-Berlin, 1984. Zbl0531.47014MR1335452
6. [KV] C. Kipnis and S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys., Vol. 104, 1986, pp. 1-19. Zbl0588.60058MR834478
7. [LZ] T.J. Lyons and W.A. Zheng, A crossing estimate for the canonical process on a Dirichlet space and a tightness result, Astérique, Vol. 157-158 (Colloque P. Lévy) 1988, pp. 249-271. Zbl0654.60059
8. [MR] Z.M. Ma and M. Röckner, An Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, 1992. Zbl0826.31001MR1214375
9. [MZ] P.A. Meyer and W.A. Zheng, Construction du processus de Nelson reversible, Sém. Probab. XIX, Lect. Notes in Math., No 1123, 1984, pp. 12-26. Zbl0564.60075
10. [OS] H. Osada and T. Saitoh, An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains, Proba. Theory and R.F., Vol. 101, 1995, pp. 45-63. Zbl0816.60079MR1314174
11. [Va] S.R.S. Varadhan, Self diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion, Annals de l'I.H.P., Série Probab. and Stat., Vol. 31, 1 (in Memoriam C. Kipnis), 1995, pp. 273-285. Zbl0816.60093MR1340041
12. [WI] L. Wu, Functional limit theorems for additive functionals of reversible Markov processes, Pré-publication du Laboratoire de Mathématiques Appliquées, Université Blaise Pascal, 1995. 
13. [W2] L. Wu, Some notes on CLT for additive functionals of Markov processes, Prépublication du Laboratoire de Mathématiques Appliquées, Université Blaise Pascal, 1995. 
14. [Xu] L. Xu, Ph.D. dissertation, New York University, 1993. 

1. Anna Walczuk, Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric
2. Wei Liu, Yutao Ma, Spectral gap and convex concentration inequalities for birth–death processes
3. Rémi Rhodes, Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix