메뉴 건너뛰기




Volumn 44, Issue 2, 1999, Pages 254-272

On almost sure limit theorems

Author keywords

Convergence almost sure; Invariance principle; Limit theorems; Sums of independent variables; Weak dependence

Indexed keywords


EID: 0033622215     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0040585x97977562     Document Type: Article
Times cited : (28)

References (28)
  • 5
    • 0001581713 scopus 로고    scopus 로고
    • On almost sure limit theorems
    • in Russian
    • I. A. IBRAGIMOV, On almost sure limit theorems, Dokl. Akad. Nauk, 350 (1996), pp. 301-303 (in Russian).
    • (1996) Dokl. Akad. Nauk , vol.350 , pp. 301-303
    • Ibragimov, I.A.1
  • 7
    • 0001800016 scopus 로고
    • Gaussian random functions
    • Kluwer, Dordrecht, The Netherlands
    • M. A. LIFSHITS, Gaussian Random Functions, Math. and Its Appl. 322, Kluwer, Dordrecht, The Netherlands, 1995.
    • (1995) Math. and Its Appl. , vol.322
    • Lifshits, M.A.1
  • 8
    • 0000033355 scopus 로고
    • Convergence of random processes and limit theorems in probability theory
    • YU. V. PROKHOROV, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl., 1 (1956), pp. 157-214.
    • (1956) Theory Probab. Appl. , vol.1 , pp. 157-214
    • Prokhorov, Yu.V.1
  • 10
    • 0001818991 scopus 로고
    • On a limit pass from a sequence of sums of independent random variables to a homogeneous random process with independent increments
    • in Russian
    • A. V. SKOROKHOD, On a limit pass from a sequence of sums of independent random variables to a homogeneous random process with independent increments, Dokl. Akad. Nauk SSSR, 104 (1955), pp. 364-367 (in Russian).
    • (1955) Dokl. Akad. Nauk SSSR , vol.104 , pp. 364-367
    • Skorokhod, A.V.1
  • 12
    • 0000138369 scopus 로고
    • Théorème central limite presque sûr et la loi du logarithme itéré pour des sommes de variables aléatoires indépendantes
    • M. ATLAGH, Théorème central limite presque sûr et la loi du logarithme itéré pour des sommes de variables aléatoires indépendantes, C. R. Acad. Sci. Paris Ser. I Math., 316 (1993), pp. 929-932.
    • (1993) C. R. Acad. Sci. Paris Ser. I Math. , vol.316 , pp. 929-932
    • Atlagh, M.1
  • 13
    • 0001929260 scopus 로고    scopus 로고
    • Une nouvelle loi forte des grands nombres
    • V. Bergelson et al., eds., de Gruyter, Berlin
    • M. ATLAGH AND M. WEBER, Une nouvelle loi forte des grands nombres, in Convergence in Ergodic Theory and Probability, V. Bergelson et al., eds., de Gruyter, Berlin, 1996, pp. 41-62.
    • (1996) Convergence in Ergodic Theory and Probability , pp. 41-62
    • Atlagh, M.1    Weber, M.2
  • 14
    • 21844522401 scopus 로고
    • On the almost sure central lirait theorem and domains of attraction
    • I. BERKES, On the almost sure central lirait theorem and domains of attraction, Probab. Theory Related Fields, 102 (1995), pp. 1-18.
    • (1995) Probab. Theory Related Fields , vol.102 , pp. 1-18
    • Berkes, I.1
  • 15
    • 0003112604 scopus 로고    scopus 로고
    • Results and problems related to the pointwise central limit theorem
    • North-Holland, Amsterdam
    • I. BERKES, Results and problems related to the pointwise central limit theorem, in Asymptotic Methods in Probability and Statistics, North-Holland, Amsterdam, 1998, pp. 59-96.
    • (1998) Asymptotic Methods in Probability and Statistics , pp. 59-96
    • Berkes, I.1
  • 16
    • 0001079407 scopus 로고
    • Some limit theorems in log density
    • I. BERKES AND H. DEHLING, Some limit theorems in log density, Ann. Probab., 21 (1993), pp. 1640-1670.
    • (1993) Ann. Probab. , vol.21 , pp. 1640-1670
    • Berkes, I.1    Dehling, H.2
  • 17
    • 84976180582 scopus 로고
    • An almost everywhere central limit theorem
    • G. A. BROSAMLER, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc., 104 (1988), pp. 561-574.
    • (1988) Math. Proc. Cambridge Philos. Soc. , vol.104 , pp. 561-574
    • Brosamler, G.A.1
  • 19
    • 0001618801 scopus 로고
    • A note on the almost sure central limit theorem
    • M. LACEY AND W. PHILIPP, A note on the almost sure central limit theorem, Statist. Probab. Lett., 9 (1990), pp. 201-205.
    • (1990) Statist. Probab. Lett. , vol.9 , pp. 201-205
    • Lacey, M.1    Philipp, W.2
  • 20
    • 0001901793 scopus 로고
    • An improvement of Strassen's invariance principle
    • P. MAJOR, An improvement of Strassen's invariance principle, Ann. Probab., 7 (1979), pp. 55-61.
    • (1979) Ann. Probab. , vol.7 , pp. 55-61
    • Major, P.1
  • 22
    • 0000232976 scopus 로고
    • A note on the almost sure central limit theorem for weakly dependent random variables
    • M. PELIGRAD AND Q.-M. SHAO, A note on the almost sure central limit theorem for weakly dependent random variables, Statist. Probab. Lett., 22 (1995), pp. 131-136.
    • (1995) Statist. Probab. Lett. , vol.22 , pp. 131-136
    • Peligrad, M.1    Shao, Q.-M.2
  • 23
    • 0000936180 scopus 로고    scopus 로고
    • On the central limit theorem for independent random variables with almost sure convergence
    • B. RODZIK AND Z. RYCHLIK, On the central limit theorem for independent random variables with almost sure convergence, Probab. Math. Statist., 16 (1996), pp. 299-309.
    • (1996) Probab. Math. Statist. , vol.16 , pp. 299-309
    • Rodzik, B.1    Rychlik, Z.2
  • 24
    • 84985410727 scopus 로고
    • On strong versions of the almost sure central limit theorem
    • P. SCHATTE, On strong versions of the almost sure central limit theorem, Math. Nachr., 137 (1988), pp. 249-256.
    • (1988) Math. Nachr. , vol.137 , pp. 249-256
    • Schatte, P.1
  • 25
    • 0000269019 scopus 로고
    • On the central limit theorem with almost sure convergence
    • P. SCHATTE, On the central limit theorem with almost sure convergence, Probab. Math. Statist., 11 (1991), pp. 237-246.
    • (1991) Probab. Math. Statist. , vol.11 , pp. 237-246
    • Schatte, P.1
  • 26
    • 0003275708 scopus 로고
    • A strong approximation for logarithmic averages of partial sums of random variables
    • G. HURELBAATAR, A strong approximation for logarithmic averages of partial sums of random variables, Period. Math. Hungar., 31 (1995), pp. 189-200.
    • (1995) Period. Math. Hungar. , vol.31 , pp. 189-200
    • Hurelbaatar, G.1
  • 27
    • 0032518006 scopus 로고    scopus 로고
    • Almost sure central limit theorem under minimal conditions
    • I. BERKES, E. CSÁKI, AND L. HORVÁTH, Almost sure central limit theorem under minimal conditions, Statist. Probab. Lett., 37 (1998), pp. 67-76.
    • (1998) Statist. Probab. Lett. , vol.37 , pp. 67-76
    • Berkes, I.1    Csáki, E.2    Horváth, L.3
  • 28
    • 0032533062 scopus 로고    scopus 로고
    • On the convergence of generalized moments in almost sure central limit theorems
    • I. A. IBRAGIMOV AND M. A. LIFSHITS, On the convergence of generalized moments in almost sure central limit theorems, Statist. Probab. Lett., 40 (1998), pp. 343-351.
    • (1998) Statist. Probab. Lett. , vol.40 , pp. 343-351
    • Ibragimov, I.A.1    Lifshits, M.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.