Français
On the weak invariance principle and its quenched version under projective criteria
Post-edited
Authors : Merlevède, Florence (Author of the conference)
CIRM (Publisher )
60F05 - Central limit and other weak theorems
60F17 - Functional limit theorems; invariance principles
CIRM (Publisher )
Abstract :
In this talk, we shall first review some projective criteria under which the central limit theorem holds. The projective criteria considered will be the Heyde criterion, the Hannan criterion, the Maxwell-Woodroofe condition and the Dedecker-Rio's condition. We shall also investigate under which projective criteria the reinforced versions of the CLT such as the weak invariance principle or the quenched CLT (and its functional form) still hold.
MSC Codes : 60F05 - Central limit and other weak theorems
60F17 - Functional limit theorems; invariance principles
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 22/07/14 Conference Date : 08/07/14 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : QuickTime (.mov) Video Time : 00:51:46 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-07-08_Merlevede.mp4 
|
Information on the Event
Event Title : Limit theorems in dynamics and applications / Théorèmes limites en dynamique et applicationsEvent Organizers : Olla, Stefano ; Reinert, Gesine ; Vaienti, Sandro ; Volny, Dalibor Dates : 07/07/14 - 11/07/14 Event Year : 2014
Citation Data
DOI : 10.24350/CIRM.V.18538103Cite this video as: Merlevède, Florence (2014). On the weak invariance principle and its quenched version under projective criteria. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18538103 URI : http://dx.doi.org/10.24350/CIRM.V.18538103 |
Bibliography
- Borodin, A.N. and Ibragimov, I.A. Limit theorems for functionals of random walks. Trudy Mat. Inst. Steklov. 195. (1994). Transl. into English: Proc. Steklov Inst. Math. (1995) - https://www.zbmath.org/?q=an:0855.60001
- Bradley, R. C. On quantiles and the central limit question for strongly mixing sequences. Dedicated to Murray Rosenblatt. J. Theoret. Probab. 10 (1997), 507-555 - https://www.zbmath.org/?q=an:0887.60028
- Chen, X. Limit theorems for functionals of ergodic Markov chains with general state space. Memoirs of the AMS, 139 nr 664 (1999) - http://dx.doi.org/10.1090/memo/0664
- Cuny, C. and Merlevede, F. On martingale approximations and the quenched weak invariance principle. Ann. Probab. 42 (2014), 760-793 - http://dx.doi.org/10.1214/13-aop856
- Cuny, C. and Peligrad, M. Central limit theorem started at a point for stationary processes and additive functionals of reversible Markov chains. J. Theor. Probability. 25 (2012), 171-188 - http://dx.doi.org/10.1007/s10959-010-0321-8
- Cuny, C. and Volny, D. A quenched invariance principle for stationary processes. arXiv:1202.4875, accepted for publication in ALEA Lat. Am. J. Probab. Math. Stat. (2012) - https://www.zbmath.org/?q=an:1277.60056
- Dedecker, J., Merlevede, F. and Peligrad, M. A quenched weak invariance principle. Ann. Inst. H. Poincare Probab. Statist. 50 (2014), 872-898 - http://dx.doi.org/10.1214/13-aihp553
- Dedecker, J., Merlevede, F. and Volny, D. On the weak invariance principle for non- adapted sequences under projective criteria. J. Theoret. Probab. 20 (2007), 971-1004 - http://dx.doi.org/10.1007/s10959-007-0090-1
- Dedecker, J. and Rio, E. On the functional central limit theorem for stationary processes, Ann. Inst. H. Poincare Probab. Statist. 36 (2000), 1-34 - https://www.zbmath.org/?q=an:0949.60049
- Derriennic, Y. and Lin, M. The central limit theorem for Markov chains with normal transition operators, started at a point. Probab. Theory Relat. Fields. 119 (2001), 508- 528 - http://dx.doi.org/10.1007/pl00008769
- Derriennic, Y. and Lin, M. The central limit theorem for Markov chains started at a point, Probab. Theory Relat. Fields. 125 (2003), 73-76 - http://dx.doi.org/10.1007/s004400200215
- Doukhan, P., Massart, P. and Rio, E. The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincare Probab. Statist. 30 (1994), 63-82 - https://www.zbmath.org/?q=an:0790.60037
- Durieu, O. Independence of four projective criteria for the weak invariance principle. ALEA Lat. Am. J. Probab. Math. Stat. 5 (2009), 21-26 - https://www.zbmath.org/?q=an:1169.60005
- Durieu, O. and Volny, D. Comparison between criteria leading to the weak invariance principle. Ann. Inst. Henri Poincare Probab. Stat. 44 (2008), 324-340 - http://dx.doi.org/10.1214/07-aihp123
- Gordin, M. I. and Lifsic, B. A. The central limit theorem for stationary Markov processes, Soviet Math. Dokl. 19 (1978), 392-394 - https://www.zbmath.org/?q=an:0395.60057
- Gordin, M. and Peligrad, M. On the functional central limit theorem via martingale approximation. Bernoulli 17 (2011), 424-440 - http://dx.doi.org/10.3150/10-bej276
- Hannan, E. J. The central limit theorem for time series regression. Stoch. Processes Appl. 9 (1979), 281-289 - http://dx.doi.org/10.1016/0304-4149(79)90050-4
- Heyde, C. C. On the central limit theorem for stationary processes. Z. Wahrsch. verw. Gebiete. 30 (1974), 315-320 - http://dx.doi.org/10.1007/bf00532619
- Heyde, C. C. On the central limit theorem and iterated logarithm law for stationary processes. Bull. Austral. Math. Soc. 12 (1975), 1-8 - http://dx.doi.org/10.1017/s0004972700023583
- Kipnis, C., Varadhan, S.R.S.. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Commun. Math. Phys. 104 (1986), 1-19 - http://dx.doi.org/10.1007/bf01210789
- Maxwell, M. and Woodroofe, M. Central limit theorem for additive fonctionals of Markov chains. Ann. Probab. 28 (2000), 713-724 - http://dx.doi.org/10.1214/aop/1019160258
- Volny, D. and Woodroofe, M. An example of non-quenched convergence in the conditional central limit theorem for partial sums of a linear process. Dependence in analysis, probability and number theory (The Phillipp memorial volume), Kendrick Press. 317-323, (2010) - https://www.zbmath.org/?q=an:1213.60051
- Wu, W.-B. and Woodroofe, M. Martingale approximations for sums of stationary processes. Ann. Probab. 32 (2004), 1674-1690 - http://dx.doi.org/10.1214/009117904000000351
- Zhao, O. and Woodroofe, M. On martingale approximations. Ann. Appl. Probab. 18 (2008), 1831-1847 - http://dx.doi.org/10.1214/07-aap505
