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Volumn 110, Issue 3, 1998, Pages 397-426

A central limit theorem for stationary random fields

Author keywords

Central limit theorem; Stationary random fields

Indexed keywords


EID: 0032023978     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050153     Document Type: Article
Times cited : (72)

References (29)
  • 1
    • 0001007401 scopus 로고
    • The lindeberg-lévy theorem for martingales
    • Billingsley, P.: The Lindeberg-Lévy theorem for martingales, Proc. Amer. Math. Soc. 12, 788-792 (1961)
    • (1961) Proc. Amer. Math. Soc. , vol.12 , pp. 788-792
    • Billingsley, P.1
  • 2
    • 0000963886 scopus 로고
    • On the central limit theorem for stationary mixing random fields
    • Bolthausen, E.: On the central limit theorem for stationary mixing random fields, Ann. Probab. 10, 1047-1050 (1982)
    • (1982) Ann. Probab. , vol.10 , pp. 1047-1050
    • Bolthausen, E.1
  • 4
    • 0003155075 scopus 로고
    • Mixing: Properties and examples
    • Springer, Berlin
    • Doukhan, P.: Mixing: Properties and Examples. Lecture Notes in Statist. Vol. 85, (Springer, Berlin, 1994)
    • (1994) Lecture Notes in Statist. , vol.85
    • Doukhan, P.1
  • 5
    • 0005386802 scopus 로고
    • Remarks on the CLT for weakly dependent random variables
    • Springer, Berlin
    • Dürr, D. and Goldstein, S.: Remarks on the CLT for weakly dependent random variables. Lecture Notes in Math. No. 1158 (Springer, Berlin, 1984)
    • (1984) Lecture Notes in Math. , Issue.1158
    • Dürr, D.1    Goldstein, S.2
  • 6
    • 0039683580 scopus 로고
    • Martingale convergence to mixture of infinitely divisible laws
    • Eagleason, G.K.: Martingale convergence to mixture of infinitely divisible laws, Ann. Probab. 3, 557-562 (1975)
    • (1975) Ann. Probab. , vol.3 , pp. 557-562
    • Eagleason, G.K.1
  • 7
    • 0001309929 scopus 로고
    • Sur la distance de deux lois de probabilité
    • Fréchet, M.: Sur la distance de deux lois de probabilité, C.R Acad. Sci. Paris. 244, No 6, 689-692 (1957)
    • (1957) C.R Acad. Sci. Paris , vol.244 , Issue.6 , pp. 689-692
    • Fréchet, M.1
  • 9
    • 0000282259 scopus 로고
    • The central limit theorem for stationary processes
    • Gordin, M.I.: The central limit theorem for stationary processes, Soviet Math. Dokl. 10, 1174-1176 (1969)
    • (1969) Soviet Math. Dokl. , vol.10 , pp. 1174-1176
    • Gordin, M.I.1
  • 11
    • 0039683579 scopus 로고
    • Homoclinic approach to the central limit theorem for dynamical systems
    • American mathematical society
    • Gordin, M.I.: Homoclinic approach to the central limit theorem for dynamical systems, Contempt. Math. 149, 149-162 (American mathematical society, 1993)
    • (1993) Contempt. Math. , vol.149 , pp. 149-162
    • Gordin, M.I.1
  • 15
    • 0000636504 scopus 로고
    • Some limit theorems for stationary processes
    • Ibragimov, I.A.: Some limit theorems for stationary processes, Theory Probab. Appl. 7, 349-382 (1962)
    • (1962) Theory Probab. Appl. , vol.7 , pp. 349-382
    • Ibragimov, I.A.1
  • 16
    • 0002237639 scopus 로고
    • A central limit theorem for a class of dependent random variables
    • Ibragimov, I.A.: A central limit theorem for a class of dependent random variables, Theory Probab. Appl. 8, 83-89 (1963)
    • (1963) Theory Probab. Appl. , vol.8 , pp. 83-89
    • Ibragimov, I.A.1
  • 18
    • 0039471453 scopus 로고
    • A central limit theorem for stationary random fields
    • Janžura, M. and Lachout, P: A central limit theorem for stationary random fields, Mathematical Method of Statistics 4, 463-471 (1995)
    • (1995) Mathematical Method of Statistics , vol.4 , pp. 463-471
    • Janžura, M.1    Lachout, P.2
  • 19
    • 0000716774 scopus 로고
    • On asymptotic normality of pseudo likehood estimates for pairwise interaction processes
    • Jensen, J.L. and Künsch, H.R.: On asymptotic normality of pseudo likehood estimates for pairwise interaction processes, Ann. Inst. Statist. Math. 46, 475-486 (1994)
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 475-486
    • Jensen, J.L.1    Künsch, H.R.2
  • 20
    • 34250956889 scopus 로고
    • Eine neue herleitung des exponentialgezetzes in der wahrscheinlichkeitsrechnung
    • Lindeberg, J.W.: Eine neue Herleitung des Exponentialgezetzes in der Wahrscheinlichkeitsrechnung, Mathematische Zeitschrift 15, 211-225 (1922)
    • (1922) Mathematische Zeitschrift , vol.15 , pp. 211-225
    • Lindeberg, J.W.1
  • 21
    • 0010067722 scopus 로고
    • Billingsley-Ibragimov theorem for martingale-difference random fields and its applications to some models of classical statistical physics
    • Série I
    • Nahapetian, B.: Billingsley-Ibragimov theorem for martingale-difference random fields and its applications to some models of classical statistical physics. C. R. Acad. Sci. Paris. 320, Série I. 1539-1544 (1995)
    • (1995) C. R. Acad. Sci. Paris , vol.320 , pp. 1539-1544
    • Nahapetian, B.1
  • 22
    • 0000352449 scopus 로고
    • Martingale-difference Gibbs random fields and central limit theorem
    • Series A-I
    • Nahapetian, B. and Petrosian, A.N.: Martingale-difference Gibbs random fields and central limit theorem. Ann. Acad. Sci. Fennicae, Series A-I. 17, 105-110 (1992)
    • (1992) Ann. Acad. Sci. Fennicae , vol.17 , pp. 105-110
    • Nahapetian, B.1    Petrosian, A.N.2
  • 23
    • 0005318365 scopus 로고
    • A note on two measures of dependence and mixing sequences
    • Peligrad, M: A note on two measures of dependence and mixing sequences, Adv. Appl. Prob. 15, 461-464 (1983)
    • (1983) Adv. Appl. Prob. , vol.15 , pp. 461-464
    • Peligrad, M.1
  • 25
    • 0000951165 scopus 로고
    • On stable sequences of events
    • Rényi, A: On stable sequences of events, Sankhyā Ser. A 25, 189-206 (1963)
    • (1963) Sankhyā Ser. A , vol.25 , pp. 189-206
    • Rényi, A.1
  • 26
    • 0000121117 scopus 로고
    • Covariance inequalities for strongly mixing processes
    • Rio, E: Covariance inequalities for strongly mixing processes, Ann. Inst. Henri Poincaré Vol 29. 4, 587-597 (1993)
    • (1993) Ann. Inst. Henri Poincaré , vol.29 , Issue.4 , pp. 587-597
    • Rio, E.1
  • 27
    • 0010044797 scopus 로고
    • About the lindeberg method for strongly mixing sequences
    • Rio, E: About the Lindeberg method for strongly mixing sequences. ESAIM. Vol. 1, 35-61 (1995)
    • (1995) ESAIM , vol.1 , pp. 35-61
    • Rio, E.1
  • 28
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation of a sum of dependent random variables
    • Stein, C: A bound for the error in the normal approximation of a sum of dependent random variables, Proc. Sixth Berkeley Symp. Math. Statist, and Probab. 2, 583-602 (1973)
    • (1973) Proc. Sixth Berkeley Symp. Math. Statist, and Probab. , vol.2 , pp. 583-602
    • Stein, C.1
  • 29
    • 0001795008 scopus 로고
    • Approximating martingales and the central limit theorem for strictly stationary processes
    • Volný, D: Approximating martingales and the central limit theorem for strictly stationary processes, Stoch. Processes Appl. 44, 41-74 (1993)
    • (1993) Stoch. Processes Appl. , vol.44 , pp. 41-74
    • Volný, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.