메뉴 건너뛰기




Volumn 13, Issue , 2008, Pages 302-310

Exact convergence rate for the maximum of standardized gaussian increments

Author keywords

Almost sure limit theorem; Gaussian random walk; Integral test; L vy s continuity modulus; Multiscale statistic; Standardized increments

Indexed keywords


EID: 45849110727     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v13-1380     Document Type: Article
Times cited : (8)

References (19)
  • 1
    • 0009071603 scopus 로고
    • On the upper and lower classes for a stationary Gaussian stochastic process
    • J. M. P. Albin On the upper and lower classes for a stationary Gaussian stochastic process. Ann. Probab. 22(1994), 77-93.
    • (1994) Ann. Probab , vol.22 , pp. 77-93
    • Albin, J.M.P.1
  • 2
    • 45849153436 scopus 로고    scopus 로고
    • Consistencies and rates of convergence of jump penalized least squares estimators
    • to appear
    • L. Boysen, A. Kempe, A. Munk, V. Liebscher, O. Wittich. Consistencies and rates of convergence of jump penalized least squares estimators. Ann. Statist. (2007), to appear.
    • (2007) Ann. Statist.
    • Boysen, L.1    Kempe, A.2    Munk, A.3    Liebscher, V.4    Wittich, O.5
  • 3
    • 33644942655 scopus 로고    scopus 로고
    • Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices
    • H. P. Chan, T. L. Lai. Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices. Ann. Probab. 34(2006), 80-121.
    • (2006) Ann. Probab , vol.34 , pp. 80-121
    • Chan, H.P.1    Lai, T.L.2
  • 4
    • 84988115122 scopus 로고
    • On the Lipschitz’s condition for Brownian motion
    • K.L. Chung, P. Erdös, T. Sirao. On the Lipschitz’s condition for Brownian motion. J. Math. Soc. Japan 11(1959), 263-274.
    • (1959) J. Math. Soc. Japan , vol.11 , pp. 263-274
    • Chung, K.L.1    Erdös, P.2    Sirao, T.3
  • 5
    • 0035608644 scopus 로고    scopus 로고
    • Local extremes, runs, strings and multiresolution
    • P.L. Davies, A. Kovac. Local extremes, runs, strings and multiresolution. Ann. Statist. 29(2001), 1-65.
    • (2001) Ann. Statist. , vol.29 , pp. 1-65
    • Davies, P.L.1    Kovac, A.2
  • 6
    • 0000090342 scopus 로고
    • Limit laws of Erdös-Rényi-Shepp type
    • P. Deheuvels, L. Devroye. Limit laws of Erdös-Rényi-Shepp type. Ann. Probab. 15(1987), 1363-1386.
    • (1987) Ann. Probab , vol.15 , pp. 1363-1386
    • Deheuvels, P.1    Devroye, L.2
  • 7
    • 0000040722 scopus 로고
    • Exact convergence rate in the limit theorems of Erdoos-Renyi and Shepp
    • P. Deheuvels, L. Devroye, J. Lynch. Exact convergence rate in the limit theorems of Erdoos-Renyi and Shepp. Ann. Probab. 14(1986), 209-223.
    • (1986) Ann. Probab. , vol.14 , pp. 209-223
    • Deheuvels, P.1    Devroye, L.2    Lynch, J.3
  • 8
    • 0035592604 scopus 로고    scopus 로고
    • Multiscale testing of qualitative hypotheses
    • L. Diimbgen, V.G. Spokoiny. Multiscale testing of qualitative hypotheses. Ann. Statist. 29(2001), 124-152.
    • (2001) Ann. Statist , vol.29 , pp. 124-152
    • Diimbgen, L.1    Spokoiny, V.G.2
  • 10
    • 0003910552 scopus 로고
    • Extremes and related properties of random sequences and processes
    • New York-Heidelberg-Berlin: Springer-Verlag
    • M.R. Leadbetter, G. Lindgren, H. Rootzén. Extremes and related properties of random sequences and processes. Springer Series in Statistics (1983). New York-Heidelberg-Berlin: Springer-Verlag.
    • (1983) Springer Series in Statistics
    • Leadbetter, M.R.1    Lindgren, G.2    Rootzén, H.3
  • 11
    • 84968466726 scopus 로고
    • A law of iterated logarithm for stationary Gaussian processes
    • P.K. Pathak, C. Qualls. A law of iterated logarithm for stationary Gaussian processes. Trans. Amer. Math. Soc. 181(1973), 185-193.
    • (1973) Trans. Amer. Math. Soc , vol.181 , pp. 185-193
    • Pathak, P.K.1    Qualls, C.2
  • 12
    • 0142015766 scopus 로고
    • An iterated logarithm law for the maximum in a stationary Gaussian sequence
    • J. Pickands. An iterated logarithm law for the maximum in a stationary Gaussian sequence. Z. Wahrscheinlichkeitstheorie verw. Geb. 12(1969), 344-353.
    • (1969) Z. Wahrscheinlichkeitstheorie Verw. Geb , vol.12 , pp. 344-353
    • Pickands, J.1
  • 13
    • 0000128872 scopus 로고
    • On the increments of Wiener and related processes
    • P. Révész. On the increments of Wiener and related processes. Ann. Probab. 10(1982), 613-622.
    • (1982) Ann. Probab , vol.10 , pp. 613-622
    • Révész, P.1
  • 14
    • 0001045155 scopus 로고
    • On a conjecture of Révész
    • Q.-M. Shao. On a conjecture of Révész. Proc. Amer. Math. Soc. 123(1995), 575-582.
    • (1995) Proc. Amer. Math. Soc , vol.123 , pp. 575-582
    • Shao, Q.-M.1
  • 15
    • 21844489952 scopus 로고
    • Using the generalized likelihood ratio statistic for sequential detection of a change-point
    • D. Siegmund, E. S. Venkatraman. Using the generalized likelihood ratio statistic for sequential detection of a change-point. Ann. Statist. 23(1995), 255-271.
    • (1995) Ann. Statist. , vol.23 , pp. 255-271
    • Siegmund, D.1    Venkatraman, E.S.2
  • 16
    • 0003265138 scopus 로고    scopus 로고
    • Tail probabilities for the null distribution of scanning statistics
    • D. Siegmund, B. Yakir. Tail probabilities for the null distribution of scanning statistics. Bernoulli 6(2000), 191-213.
    • (2000) Bernoulli , vol.6 , pp. 191-213
    • Siegmund, D.1    Yakir, B.2
  • 17
    • 0005364788 scopus 로고    scopus 로고
    • On a conjecture of Révész and its analogue for renewal processes
    • B. Szyszkowicz (ed.), An international conference at Carleton Univ., Canada, Amsterdam: North-Holland/Elsevier
    • J. Steinebach. On a conjecture of Révész and its analogue for renewal processes, in: B. Szyszkowicz (ed.), Asymptotic methods in probability and statistics. A volume in honour of Miklos Csorgo. An international conference at Carleton Univ., Canada, 1997. Amsterdam: North-Holland/Elsevier.
    • (1997) Asymptotic Methods in Probability and Statistics. A Volume in Honour of Miklos Csorgo.
    • Steinebach, J.1
  • 18
    • 0039221472 scopus 로고
    • The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Brownian motion
    • C. Qualls. The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Brownian motion. Ann. Probab. 5(1977), 724-739.
    • (1977) Ann. Probab , vol.5 , pp. 724-739
    • Qualls, C.1
  • 19
    • 0040542076 scopus 로고
    • An asymptotic 0-1 behavior of Gaussian processes
    • C. Qualls, H. Watanabe. An asymptotic 0-1 behavior of Gaussian processes. Ann. Math. Statist. 42(1971), 2029-2035.
    • (1971) Ann. Math. Statist , vol.42 , pp. 2029-2035
    • Qualls, C.1    Watanabe, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.