메뉴 건너뛰기




Volumn 108, Issue 2, 2003, Pages 229-262

The conditional central limit theorem in Hilbert spaces

Author keywords

Central limit theorem; Hilbert space; Linear processes; Mixingale; Stable convergence; Strictly stationary process; Strong mixing; Weak invariance principle

Indexed keywords


EID: 0142119373     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2003.07.004     Document Type: Article
Times cited : (38)

References (38)
  • 1
    • 0002478027 scopus 로고
    • On mixing and stability of limit theorems
    • Aldous D.J. Eagleson G.K. On mixing and stability of limit theorems Ann. Probab. 6 1978 325-331
    • (1978) Ann. Probab. , vol.6 , pp. 325-331
    • Aldous, D.J.1    Eagleson, G.K.2
  • 4
    • 0142014447 scopus 로고    scopus 로고
    • Approximate martingale central limit theorems on Hilbert space
    • Bingham M.S. Approximate martingale central limit theorems on Hilbert space C.R. Math. Rep. Acad. Sci. Canada 22 2000 111-117
    • (2000) C.R. Math. Rep. Acad. Sci. Canada , vol.22 , pp. 111-117
    • Bingham, M.S.1
  • 5
    • 0013172178 scopus 로고    scopus 로고
    • Linear Processes in Function Spaces. Theory and Applications
    • Berlin: Springer
    • Bosq D. Linear Processes in Function Spaces. Theory and Applications Lecture Notes in Statistics Vol. 149 2000 Springer Berlin
    • (2000) Lecture Notes in Statistics , vol.149
    • Bosq, D.1
  • 6
    • 0031490760 scopus 로고    scopus 로고
    • On quantiles and the central limit question for strongly mixing sequences
    • Bradley R.C. On quantiles and the central limit question for strongly mixing sequences J. Theoret. Probab. 10 1997 507-555
    • (1997) J. Theoret. Probab. , vol.10 , pp. 507-555
    • Bradley, R.C.1
  • 8
    • 0032343669 scopus 로고    scopus 로고
    • Central limit and functional central limit theorems for Hilbert-valued dependent heterogeneous arrays with applications
    • Chen X. White H. Central limit and functional central limit theorems for Hilbert-valued dependent heterogeneous arrays with applications Econometric Theory 14 1998 260-284
    • (1998) Econometric Theory , vol.14 , pp. 260-284
    • Chen, X.1    White, H.2
  • 9
    • 0000137215 scopus 로고
    • Mixing conditions for Markov chains
    • Davydov Yu.A. Mixing conditions for Markov chains Theory Probab. Appl. 18 1973 312-328
    • (1973) Theory Probab. Appl. , vol.18 , pp. 312-328
    • Davydov, Yu.A.1
  • 10
  • 11
    • 0036631350 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for the conditional central limit theorem
    • Dedecker J. Merlevède F. Necessary and sufficient conditions for the conditional central limit theorem Ann. Probab. 30 2002 1044-1081
    • (2002) Ann. Probab. , vol.30 , pp. 1044-1081
    • Dedecker, J.1    Merlevède, F.2
  • 12
    • 0033633561 scopus 로고    scopus 로고
    • On the functional central limit theorem for stationary processes
    • Dedecker J. Rio E. On the functional central limit theorem for stationary processes Ann. Inst. H. Poincaré Probab. Statist. 36 2000 1-34
    • (2000) Ann. Inst. H. Poincaré Probab. Statist. , vol.36 , pp. 1-34
    • Dedecker, J.1    Rio, E.2
  • 13
    • 0005276893 scopus 로고
    • Limit theorems for sums of weakly dependent Banach space valued random variables
    • Dehling H. Limit theorems for sums of weakly dependent Banach space valued random variables Z. Wahrsch. Verw. Gebiete 63 1983 393-432
    • (1983) Z. Wahrsch. Verw. Gebiete , vol.63 , pp. 393-432
    • Dehling, H.1
  • 15
    • 0005277120 scopus 로고
    • Some simple conditions for limit theorems to be mixing
    • Eagleson G.K. Some simple conditions for limit theorems to be mixing Teor. Verojatnost. i Primenen. 21 1976 653-660
    • (1976) Teor. Verojatnost. I Primenen. , vol.21 , pp. 653-660
    • Eagleson, G.K.1
  • 16
    • 0001309929 scopus 로고
    • Sur la distance de deux loi de probabilité
    • Fréchet M. Sur la distance de deux loi de probabilité C.R. Acad. Sci. Paris 244 1957 689-692
    • (1957) C.R. Acad. Sci. Paris , vol.244 , pp. 689-692
    • Fréchet, M.1
  • 17
    • 0005337807 scopus 로고
    • The central limit theorem for stationary processes
    • Gordin M.I. The central limit theorem for stationary processes Dokl. Akad. Nauk SSSR 188 1969 739-741
    • (1969) Dokl. Akad. Nauk SSSR , vol.188 , pp. 739-741
    • Gordin, M.I.1
  • 20
    • 0005380313 scopus 로고
    • On the central limit theorem for stationary processes
    • Heyde C.C. On the central limit theorem for stationary processes Z. Wahrsch. Verw. Gebiete 30 1974 315-320
    • (1974) Z. Wahrsch. Verw. Gebiete , vol.30 , pp. 315-320
    • Heyde, C.C.1
  • 21
    • 0000121609 scopus 로고
    • The law of large numbers and the central limit theorem in Banach spaces
    • Hoffman-Jorgensen J. Pisier G. The law of large numbers and the central limit theorem in Banach spaces Ann. Probab. 4 1976 587-599
    • (1976) Ann. Probab. , vol.4 , pp. 587-599
    • Hoffman-Jorgensen, J.1    Pisier, G.2
  • 24
    • 0142078175 scopus 로고
    • On limit theorems for sums of dependent Hilbert space valued random variables
    • Springer, New York
    • Jakubowski, A., 1980. On limit theorems for sums of dependent Hilbert space valued random variables. In: Lecture Notes in Statistics, Vol. 2. Springer, New York, pp. 178-187.
    • (1980) Lecture Notes in Statistics , vol.2 , pp. 178-187
    • Jakubowski, A.1
  • 25
    • 0039336819 scopus 로고
    • The invariance principle for Banach space valued random variables
    • Kuelbs J. The invariance principle for Banach space valued random variables J. Multivariate Anal. 3 1973 161-172
    • (1973) J. Multivariate Anal. , vol.3 , pp. 161-172
    • Kuelbs, J.1
  • 26
    • 0542387874 scopus 로고
    • Invariance principles for dependent variables
    • McLeish D.L. Invariance principles for dependent variables Z. Wahrsch. Verw. Gebiete 32 1975 165-178
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 165-178
    • McLeish, D.L.1
  • 27
    • 0001915127 scopus 로고
    • A maximal inequality and dependent strong laws
    • McLeish D.L. A maximal inequality and dependent strong laws Ann. Probab. 3 1975 829-839
    • (1975) Ann. Probab. , vol.3 , pp. 829-839
    • McLeish, D.L.1
  • 28
    • 0001915131 scopus 로고
    • On the invariance principle for non stationary mixingales
    • McLeish D.L. On the invariance principle for non stationary mixingales Ann. Probab. 5 1977 616-621
    • (1977) Ann. Probab. , vol.5 , pp. 616-621
    • McLeish, D.L.1
  • 29
    • 0001224368 scopus 로고
    • Sur l'inversibilité des processus linéaires à valeurs dans un espace de Hilbert
    • Série I
    • Merlevède F. Sur l'inversibilité des processus linéaires à valeurs dans un espace de Hilbert C.R. Acad. Sci. Paris 321 Série I 1995 477-480
    • (1995) C.R. Acad. Sci. Paris , vol.321 , pp. 477-480
    • Merlevède, F.1
  • 30
    • 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
    • To appear
    • 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. Theor. Probab., to appear.
    • (2003) J. Theor. Probab.
    • Merlevède, F.1
  • 31
    • 0034214586 scopus 로고    scopus 로고
    • The functional central limit theorem for strong mixing sequences of random variables
    • Merlevède F. Peligrad M. The functional central limit theorem for strong mixing sequences of random variables Ann. Probab. 28 3 2000 1336-1352
    • (2000) Ann. Probab. , vol.28 , Issue.3 , pp. 1336-1352
    • Merlevède, F.1    Peligrad, M.2
  • 32
    • 0042231922 scopus 로고    scopus 로고
    • Sharp conditions for the CLT of linear processes in a Hilbert space
    • Merlevède F. Peligrad M. Utev S. Sharp conditions for the CLT of linear processes in a Hilbert space J. Theor. Probab. 10 1997 681-693
    • (1997) J. Theor. Probab. , vol.10 , pp. 681-693
    • Merlevède, F.1    Peligrad, M.2    Utev, S.3
  • 33
    • 0000951165 scopus 로고
    • On stable sequences of events
    • Rényi A. On stable sequences of events Sankhyā Ser. A 25 1963 293-302
    • (1963) Sankhyā Ser. A , vol.25 , pp. 293-302
    • Rényi, A.1
  • 34
    • 0002605356 scopus 로고
    • A central limit theorem and a strong mixing condition
    • Rosenblatt M. A central limit theorem and a strong mixing condition Proc. Nat. Acad. Sci. USA 42 1956 43-47
    • (1956) Proc. Nat. Acad. Sci. USA , vol.42 , pp. 43-47
    • Rosenblatt, M.1
  • 35
    • 0000121117 scopus 로고
    • Covariance inequalities for strongly mixing processes
    • Rio E. Covariance inequalities for strongly mixing processes Ann. Inst. H. Poincaré Probab. Statist. 29 1993 587-597
    • (1993) Ann. Inst. H. Poincaré Probab. Statist. , vol.29 , pp. 587-597
    • Rio, E.1
  • 36
    • 0004116414 scopus 로고
    • 3rd Edition New York: McGraw-Hill Book Co
    • Rudin W. Real and Complex Analysis 3rd Edition 1987 McGraw-Hill Book Co. New York
    • (1987) Real and Complex Analysis
    • Rudin, W.1
  • 38
    • 0010830083 scopus 로고
    • An invariance principle for the Robbins-Monro process in a Hilbert space
    • Walk H. An invariance principle for the Robbins-Monro process in a Hilbert space Z. Wahrsch. Verw. Gebiete 39 1977 135-150
    • (1977) Z. Wahrsch. Verw. Gebiete , vol.39 , pp. 135-150
    • Walk, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.