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Volumn 102, Issue 2, 2002, Pages 285-299

Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields

Author keywords

Functional central limit theorem; Invariance principle; Kahane Khintchine inequalities; Martingale difference random fields; Metric entropy; Mixing random fields; Orlicz spaces

Indexed keywords


EID: 0036887696     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(02)00178-3     Document Type: Article
Times cited : (9)

References (26)
  • 1
    • 0001535864 scopus 로고
    • A uniform central limit theorem for set-indexed partial-sum processes with finite variance
    • Alexander, K.S., Pyke, R., 1986. A uniform central limit theorem for set-indexed partial-sum processes with finite variance. Ann. Probab. 14, 582-597.
    • (1986) Ann. Probab , vol.14 , pp. 582-597
    • Alexander, K.S.1    Pyke, R.2
  • 2
    • 0000130151 scopus 로고
    • Law of the iterated logarithm for set-indexed partial sum processes with finite variance
    • Bass, R.F., 1985. Law of the iterated logarithm for set-indexed partial sum processes with finite variance. Z. Wahrsch. verw. Gebiete 70, 591-608.
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.70 , pp. 591-608
    • Bass, R.F.1
  • 3
    • 0001700021 scopus 로고
    • A uniform central limit theorem for nonuniform φ-mixing random fields
    • Chen, D., 1991. A uniform central limit theorem for nonuniform φ-mixing random fields. Ann. Probab. 19, 636-649.
    • (1991) Ann. Probab , vol.19 , pp. 636-649
    • Chen, D.1
  • 4
    • 0032023978 scopus 로고    scopus 로고
    • A central limit theorem for stationary random fields
    • Dedecker, J., 1998. A central limit theorem for stationary random fields. Probab. Theory Relat. Fields 110, 397-426.
    • (1998) Probab. Theory Relat. Fields , vol.110 , pp. 397-426
    • Dedecker, J.1
  • 5
    • 84996131879 scopus 로고    scopus 로고
    • Exponential inequalities and functional central limit theorems for random fields
    • Dedecker, J., 2001. Exponential inequalities and functional central limit theorems for random fields. ESAIM: Probab. Statist. 5, 77-104.
    • (2001) ESAIM: Probab. Statist , vol.5 , pp. 77-104
    • Dedecker, J.1
  • 6
    • 0040545177 scopus 로고
    • Strong convexity of pressure for lattice systems of classical statistical physics
    • Dobrushin, R.L., Nahapetian, B.S., 1974. Strong convexity of pressure for lattice systems of classical statistical physics. Teoret. Mat. Fiz 20, 223-234.
    • (1974) Teoret. Mat. Fiz , vol.20 , pp. 223-234
    • Dobrushin, R.L.1    Nahapetian, B.S.2
  • 7
    • 0001813888 scopus 로고
    • An invariance principle for certain probability limit theorems
    • Donsker, M.D., 1951. An invariance principle for certain probability limit theorems. Mem. Amer. Math. Soc. 6, 1-12.
    • (1951) Mem. Amer. Math. Soc , vol.6 , pp. 1-12
    • Donsker, M.D.1
  • 8
    • 0003155075 scopus 로고
    • Mixing: Properties and Examples
    • Springer, Berlin
    • Doukhan, P., 1994. Mixing: Properties and Examples, Lecture Notes in Statistics, Vol. 85, Springer, Berlin.
    • (1994) Lecture Notes in Statistics , vol.85
    • Doukhan, P.1
  • 9
    • 0002485879 scopus 로고
    • Sample functions of the Gaussian process
    • Dudley, R.M., 1973. Sample functions of the Gaussian process. Ann. Probab. 1, 66-103.
    • (1973) Ann. Probab , vol.1 , pp. 66-103
    • Dudley, R.M.1
  • 10
    • 0010917213 scopus 로고    scopus 로고
    • Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels
    • to appear
    • El Machkouri, M., Volný, D., 2002. Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels. Ann. de l'IHP, to appear.
    • (2002) Ann. De L'IHP
    • El Machkouri, M.1    Volný, D.2
  • 11
    • 0003723490 scopus 로고
    • Gibbs Measures and Phase Transitions
    • De Gruyter, Berlin
    • Georgii, H.O., 1988. Gibbs Measures and Phase Transitions. De Gruyter, Berlin.
    • (1988)
    • Georgii, H.O.1
  • 12
    • 0000288954 scopus 로고
    • Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes
    • Goldie, C.M., Greenwood, P.E., 1986. Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes. Ann. Probab. 14, 817-839.
    • (1986) Ann. Probab , vol.14 , pp. 817-839
    • Goldie, C.M.1    Greenwood, P.E.2
  • 13
    • 0000636504 scopus 로고
    • Some limit theorems for stationary processes
    • Ibragimov, I.A., 1962. Some limit theorems for stationary processes. Theory Probab. Appl. 7, 349-382.
    • (1962) Theory Probab. Appl , vol.7 , pp. 349-382
    • Ibragimov, I.A.1
  • 14
    • 0003851494 scopus 로고
    • Some Random Series of Functions
    • Cambridge University Press, Cambridge, MA
    • Kahane, J.P., 1985. Some Random Series of Functions. Cambridge University Press, Cambridge, MA.
    • (1985)
    • Kahane, J.P.1
  • 15
    • 0001280583 scopus 로고
    • Ueber dyadische brüche
    • Khintchine, A.Y., 1923. Ueber dyadische brüche. Math. Z. 18, 109-116.
    • (1923) Math. Z , vol.18 , pp. 109-116
    • Khintchine, A.Y.1
  • 16
    • 0004041950 scopus 로고
    • Convex Functions and Orlicz Spaces
    • P. Noordhoff Ltd., Groningen, The Netherlands
    • Krasnosel'skii, M.A., Rutickii, Y.B., 1961. Convex Functions and Orlicz Spaces. P. Noordhoff Ltd., Groningen, The Netherlands.
    • (1961)
    • Krasnosel'skii, M.A.1    Rutickii, Y.B.2
  • 17
    • 0001727573 scopus 로고
    • The invariance principle for a lattice of random variables
    • Kuelbs, J., 1968. The invariance principle for a lattice of random variables. Ann. Math. Statist. 39, 382-389.
    • (1968) Ann. Math. Statist , vol.39 , pp. 382-389
    • Kuelbs, J.1
  • 18
    • 0003771756 scopus 로고
    • Probability in Banach Spaces
    • Springer, New York
    • Ledoux, M., Talagrand, M., 1991. Probability in Banach Spaces. Springer, New York.
    • (1991)
    • Ledoux, M.1    Talagrand, M.2
  • 19
    • 0001915127 scopus 로고
    • A maximal inequality and dependent strong laws
    • McLeish, D.L., 1975. A maximal inequality and dependent strong laws. Ann. Probab. 3 (5), 829-839.
    • (1975) Ann. Probab , vol.3 , Issue.5 , pp. 829-839
    • McLeish, D.L.1
  • 20
    • 0010864937 scopus 로고
    • Best constants in Kahane-Khintchine inequalities in Orlicz spaces
    • Peskir, G., 1993. Best constants in Kahane-Khintchine inequalities in Orlicz spaces. J. Multivariate Anal. 45, 183-216.
    • (1993) J. Multivariate Anal , vol.45 , pp. 183-216
    • Peskir, G.1
  • 21
    • 0003314447 scopus 로고
    • Empirical processes: Theory and applications
    • NSF-CBMS Regional Conference Series in Probability and Statistics. IMS-ASA, Hayward-Alexandria
    • Pollard, D., 1990. Empirical processes: theory and applications. NSF-CBMS Regional Conference Series in Probability and Statistics. IMS-ASA, Hayward-Alexandria.
    • (1990)
    • Pollard, D.1
  • 22
    • 0001598963 scopus 로고
    • A uniform central limit theorem for partial-sum processes indexed by sets
    • London Mathematical Society of Lecture Notes Series
    • Pyke, R., 1983. A uniform central limit theorem for partial-sum processes indexed by sets. London Mathematical Society of Lecture Notes Series, Vol. 79, pp. 219-240.
    • (1983) , vol.79 , pp. 219-240
    • Pyke, R.1
  • 23
    • 4243695384 scopus 로고    scopus 로고
    • Théorie asymptotique des processus aléatoires faiblement dépendants
    • Mathématiques et applications de la SMAI. Springer, Berlin
    • Rio, E., 2000. Théorie asymptotique des processus aléatoires faiblement dépendants. Mathématiques et applications de la SMAI. Springer, Berlin.
    • (2000)
    • Rio, E.1
  • 24
    • 0000733952 scopus 로고
    • Contributions to central limit theory for dependent variables
    • Serfling, R.J., 1968. Contributions to central limit theory for dependent variables. Ann. Math. Statist. 39 (4), 1158-1175.
    • (1968) Ann. Math. Statist , vol.39 , Issue.4 , pp. 1158-1175
    • Serfling, R.J.1
  • 25
    • 0031067271 scopus 로고    scopus 로고
    • Central limit theorems for random processes with sample paths in exponential Orlicz spaces
    • Su, Z., 1997. Central limit theorems for random processes with sample paths in exponential Orlicz spaces. Stochastic Process. Appl. 66, 1-20.
    • (1997) Stochastic Process. Appl , vol.66 , pp. 1-20
    • Su, Z.1
  • 26
    • 0001464704 scopus 로고
    • Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters
    • Wichura, M.J., 1969. Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters. Ann. Math. Statist. 40, 681-687.
    • (1969) Ann. Math. Statist , vol.40 , pp. 681-687
    • Wichura, M.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.