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Volumn 19, Issue 3, 2006, Pages 647-689

On the weak invariance principle for stationary sequences under projective criteria

Author keywords

Central limit theorem; Martingale approximation; Projective criteria; Strong mixing sequences; Weak invariance principle

Indexed keywords


EID: 33845656782     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-006-0029-y     Document Type: Article
Times cited : (20)

References (36)
  • 1
    • 0002478027 scopus 로고
    • On mixing and stability of limit theorems
    • Aldous, D. J., and Eagleson, G. K. (1978). On mixing and stability of limit theorems. Ann. Probab. 6, 325-331.
    • (1978) Ann. Probab. , vol.6 , pp. 325-331
    • Aldous, D.J.1    Eagleson, G.K.2
  • 2
    • 33845600193 scopus 로고    scopus 로고
    • Weak dependence: Models and applications
    • Dehling, H., Mikosch, T., and Sorensen M. (eds.), Birkhauser
    • Ango Nzé, P., and Doukhan, P. (2002). Weak dependence: models and applications. In Dehling, H., Mikosch, T., and Sorensen M. (eds.), Empirical process techniques for dependent data, Birkhauser.
    • (2002) Empirical Process Techniques for Dependent Data
    • Ango Nzé, P.1    Doukhan, P.2
  • 5
    • 0031490760 scopus 로고    scopus 로고
    • On quantiles and the central limit question for strongly mixing sequences
    • Bradley, R. C. (1997). On quantiles and the central limit question for strongly mixing sequences. J. Theor. Probab. 10, 507-555.
    • (1997) J. Theor. Probab. , vol.10 , pp. 507-555
    • Bradley, R.C.1
  • 6
    • 0037718654 scopus 로고    scopus 로고
    • Technical Report, Department of Mathematics, Indiana University, Bloomington. Custom Publishing of I.U., Bloomington, March 2002
    • Bradley, R. C. (2002). Introduction to Strong Mixing Conditions, Volume 1. Technical Report, Department of Mathematics, Indiana University, Bloomington. Custom Publishing of I.U., Bloomington, March 2002.
    • (2002) Introduction to Strong Mixing Conditions, Volume 1
    • Bradley, R.C.1
  • 7
    • 0037718654 scopus 로고    scopus 로고
    • Technical Report, Department of Mathematics, Indiana University, Bloomington. Custom Publishing of I.U., Bloomington, March 2003
    • Bradley, R. C. (2003). Introduction to Strong Mixing Conditions, Volume 2. Technical Report, Department of Mathematics, Indiana University, Bloomington. Custom Publishing of I.U., Bloomington, March 2003.
    • (2003) Introduction to Strong Mixing Conditions, Volume 2
    • Bradley, R.C.1
  • 8
    • 0033633561 scopus 로고    scopus 로고
    • On the functional central limit theorem for stationary processes
    • Dedecker, J., and Rio, E. (2000). On the functional central limit theorem for stationary processes. Ann. Inst. H. Poincaré Probab. Stat. 36 1-34.
    • (2000) Ann. Inst. H. Poincaré Probab. Stat. , vol.36 , pp. 1-34
    • Dedecker, J.1    Rio, E.2
  • 9
    • 0036631350 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for the conditional central limit theorem
    • Dedecker, J., and Merlevède, F. (2002). Necessary and sufficient conditions for the conditional central limit theorem. Ann. Probab. 30, 1044-1081.
    • (2002) Ann. Probab. , vol.30 , pp. 1044-1081
    • Dedecker, J.1    Merlevède, F.2
  • 10
    • 0037506138 scopus 로고    scopus 로고
    • A new covariance inequality and applications
    • Dedecker, J., and Doukhan, P. (2003). A new covariance inequality and applications. Stoch. Process Appl. 106, 63-80.
    • (2003) Stoch. Process Appl. , vol.106 , pp. 63-80
    • Dedecker, J.1    Doukhan, P.2
  • 11
    • 2942568820 scopus 로고    scopus 로고
    • Empirical process techniques for dependent data
    • Birkhäuser Boston, Boston, MA
    • Dehling, H., and Philipp, W. (2002). Empirical process techniques for dependent data. In Empirical process techniques for dependent data, Birkhäuser Boston, Boston, MA, 3-113.
    • (2002) Empirical Process Techniques for Dependent Data , pp. 3-113
    • Dehling, H.1    Philipp, W.2
  • 12
    • 0000061718 scopus 로고
    • Central limit theorems for mixing sequences of random variables under minimal conditions
    • Dehling, H., Denker, M., and Philipp, W. (1986). Central limit theorems for mixing sequences of random variables under minimal conditions. Ann. Probab, 14, 1359-1370.
    • (1986) Ann. Probab , vol.14 , pp. 1359-1370
    • Dehling, H.1    Denker, M.2    Philipp, W.3
  • 13
    • 0040072248 scopus 로고
    • Uniform integrability and the central limit theorem for strongly mixing processes
    • Eberlain, E., and Taqqu, M. S. (eds.), Oberwolfach, 1985, Birkhäuser
    • Denker, M. (1986). Uniform integrability and the central limit theorem for strongly mixing processes. In Eberlain, E., and Taqqu, M. S. (eds.), Dependence in Probability and Statistics. A Survey of Recent Results, Oberwolfach, 1985, Birkhäuser.
    • (1986) Dependence in Probability and Statistics. A Survey of Recent Results
    • Denker, M.1
  • 14
    • 0005337807 scopus 로고
    • The central limit theorem for stationary processes
    • Gordin, M. I. (1969). The central limit theorem for stationary processes. Dokl. Akad. Nauk SSSR 188, 739-741.
    • (1969) Dokl. Akad. Nauk SSSR , vol.188 , pp. 739-741
    • Gordin, M.I.1
  • 16
    • 33748042500 scopus 로고
    • The invariance principle for φ-mixing sequences
    • Herrndorf, N. (1983). The invariance principle for φ-mixing sequences. Z. Wahrsch. verw. Gebiete, 63, 97-108.
    • (1983) Z. Wahrsch. Verw. Gebiete , vol.63 , pp. 97-108
    • Herrndorf, N.1
  • 17
    • 0000636511 scopus 로고
    • Some limit theorems for stationary processes
    • Ibragimov, I. A. (1962). Some limit theorems for stationary processes. Teor. Verojatnost. i Primenen. 7, 361-392.
    • (1962) Teor. Verojatnost. I Primenen. , vol.7 , pp. 361-392
    • Ibragimov, I.A.1
  • 18
    • 0011512759 scopus 로고
    • A note on the central limit theorem for dependent random variables
    • Ibragimov, I. A. (1975). A note on the central limit theorem for dependent random variables, Theory Probab. Appl., 20 135-141.
    • (1975) Theory Probab. Appl. , vol.20 , pp. 135-141
    • Ibragimov, I.A.1
  • 20
    • 0034345591 scopus 로고    scopus 로고
    • Central limit theorems for additive functionals of Markov chains
    • Maxwell, M., and Woodroofe, M. (2000). Central limit theorems for additive functionals of Markov chains. Ann. Probab. 28, 713-724.
    • (2000) Ann. Probab. , vol.28 , pp. 713-724
    • Maxwell, M.1    Woodroofe, M.2
  • 21
    • 0542387874 scopus 로고
    • Invariance principles for dependent variables
    • McLeish, D. L. (1975a). Invariance principles for dependent variables. Z. Wahrsch. verw. Gebiete, 32, 165-178.
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 165-178
    • McLeish, D.L.1
  • 22
    • 0001915127 scopus 로고
    • A maximal inequality and dependent strong laws
    • McLeish, D. L. (1975b). A maximal inequality and dependent strong laws. Ann. Probab. 3, 829-839.
    • (1975) Ann. Probab. , vol.3 , pp. 829-839
    • McLeish, D.L.1
  • 23
    • 0142014448 scopus 로고    scopus 로고
    • On the central limit theorem and its weak invariance principle for strongly mixing sequences with values in a Hilbert space via martingale approximation
    • Merlevède, F. (2003). On the central limit theorem and its weak invariance principle for strongly mixing sequences with values in a Hilbert space via martingale approximation. J. Theoret. Probab. 16, 625-653.
    • (2003) J. Theoret. Probab. , vol.16 , pp. 625-653
    • Merlevède, F.1
  • 24
    • 0034214586 scopus 로고    scopus 로고
    • The functional central limit theorem for strong mixing sequences of random variables
    • Merlevède, F., and Peligrad, M. (2000). The functional central limit theorem for strong mixing sequences of random variables. Ann. Probab. 28(3), 1336-1352.
    • (2000) Ann. Probab. , vol.28 , Issue.3 , pp. 1336-1352
    • Merlevède, F.1    Peligrad, M.2
  • 25
    • 0000285811 scopus 로고
    • Moment inequalities and the strong laws of large numbers
    • Móricz, F. A. (1976). Moment inequalities and the strong laws of large numbers. Z. Wahrscheinlichkeitstheoreie verw. Gebiete. 35(4), 299-314.
    • (1976) Z. Wahrscheinlichkeitstheoreie Verw. Gebiete. , vol.35 , Issue.4 , pp. 299-314
    • Móricz, F.A.1
  • 26
    • 0000406514 scopus 로고
    • Invariance principles for mixing sequences of random variables
    • Peligrad, M. (1982). Invariance principles for mixing sequences of random variables. Ann. Probab. 10, 968-981.
    • (1982) Ann. Probab. , vol.10 , pp. 968-981
    • Peligrad, M.1
  • 27
    • 0002720637 scopus 로고
    • Recent advances in the central limit theorem and its weak invariance principles for mixing sequences of random variables
    • Eberlein, E., and Taqqu, M. S. (eds.), Birkhäuser, Boston
    • Peligrad, M. (1986). Recent advances in the central limit theorem and its weak invariance principles for mixing sequences of random variables. In Eberlein, E., and Taqqu, M. S. (eds.), Dependence in Probability and Statistics. A Survey of Recent Results, Birkhäuser, Boston.
    • (1986) Dependence in Probability and Statistics. A Survey of Recent Results
    • Peligrad, M.1
  • 28
    • 38249018703 scopus 로고
    • On Ibragimov-Iosifescu conjecture for φ-mixing sequences
    • Peligrad, M. (1990). On Ibragimov-Iosifescu conjecture for φ-mixing sequences. Stoch. Process. Appl. 35, 293-308.
    • (1990) Stoch. Process. Appl. , vol.35 , pp. 293-308
    • Peligrad, M.1
  • 29
    • 17044387009 scopus 로고    scopus 로고
    • A new maximal inequality and invariance principle for stationary sequences
    • Peligrad, M., and Utev, S. (2005). A new maximal inequality and invariance principle for stationary sequences. Ann. Probab. 33(2), 798-815.
    • (2005) Ann. Probab. , vol.33 , Issue.2 , pp. 798-815
    • Peligrad, M.1    Utev, S.2
  • 30
    • 0003145816 scopus 로고
    • Invariance principles for independent and weakly dependent random variables
    • Eberlein, E., and Taqqu, M. S. (eds.), Birkhäuser, Boston
    • Philipp, W. (1986). Invariance principles for independent and weakly dependent random variables. In Eberlein, E., and Taqqu, M. S. (eds.), Dependence in Probability and Statistics. A Survey of Recent Results, Birkhäuser, Boston.
    • (1986) Dependence in Probability and Statistics. A Survey of Recent Results
    • Philipp, W.1
  • 31
    • 0000951165 scopus 로고
    • On stable sequences of events
    • Rényi, A. (1963). On stable sequences of events. Sankhya Ser. A 25, 293-302.
    • (1963) Sankhya Ser. A , vol.25 , pp. 293-302
    • Rényi, A.1
  • 32
    • 10644251108 scopus 로고    scopus 로고
    • Théorie asymptotique des processus aléatoires faiblement dépendants
    • Springer
    • Rio, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants. Mathématiques et applications de la SMAI. 31 Springer.
    • (2000) Mathématiques et Applications de la SMAI , vol.31
    • Rio, E.1
  • 33
    • 0002605356 scopus 로고
    • A central limit theorem and a strong mixing condition
    • Rosenblatt, M. (1956). A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. 42, 43-47.
    • (1956) Proc. Nat. Acad. Sci. , vol.42 , pp. 43-47
    • Rosenblatt, M.1
  • 34
    • 38248999802 scopus 로고
    • Almost sure invariance principles for mixing sequences of random variables
    • Shao, Q. M. (1993). Almost sure invariance principles for mixing sequences of random variables. Stoch. Process. Appl. 48, 319-334.
    • (1993) Stoch. Process. Appl. , vol.48 , pp. 319-334
    • Shao, Q.M.1
  • 35
    • 0004200722 scopus 로고
    • Academic Press, New York, San Francisco, London
    • Stout, W. (1974). Almost Sure Convergence, Academic Press, New York, San Francisco, London.
    • (1974) Almost Sure Convergence
    • Stout, W.1
  • 36
    • 3042646584 scopus 로고    scopus 로고
    • Martingale approximations for sums of stationary processes
    • Wu, W. B., and Woodroofe, M. (2004). Martingale approximations for sums of stationary processes. Ann. Probab. 32(2), 1674-1690.
    • (2004) Ann. Probab. , vol.32 , Issue.2 , pp. 1674-1690
    • Wu, W.B.1    Woodroofe, M.2


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