Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 18
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Zhang, Yong 2014. THE LIMIT THEOREMS UNDER LOGARITHMIC AVERAGES FOR MIXING RANDOM VARIABLES. Communications of the Korean Mathematical Society, Vol. 29, Issue. 2, p. 351.


    Lin, Fuming Shi, Daimin and Jiang, Yingying 2012. Some distributional limit theorems for the maxima of Gaussian vector sequences. Computers & Mathematics with Applications, Vol. 64, Issue. 8, p. 2497.


    Hörmann, Siegfried 2006. An extension of almost sure central limit theory. Statistics & Probability Letters, Vol. 76, Issue. 2, p. 191.


    Wang, Fang and Cheng, Shi Hong 2004. Almost Sure Central Limit Theorems for Heavily Trimmed Sums. Acta Mathematica Sinica, English Series, Vol. 20, Issue. 5, p. 869.


    Berkes, István 2001. The law of large numbers with exceptional sets. Statistics & Probability Letters, Vol. 55, Issue. 4, p. 431.


    Berkes, István and Horváth, Lajos 2001. The logarithmic average of sample extremes is asymptotically normal. Stochastic Processes and their Applications, Vol. 91, Issue. 1, p. 77.


    Berkes, István and Csáki, Endre 2001. A universal result in almost sure central limit theory. Stochastic Processes and their Applications, Vol. 94, Issue. 1, p. 105.


    Berkes, I. Horváth, L. and Chen, X. 2001. Central limit theorems for logarithmic averages. Studia Scientiarum Mathematicarum Hungarica, Vol. 38, Issue. 1-4, p. 79.


    Chaabane, F. 2001. INVARIANCE PRINCIPLES WITH LOGARITHMIC AVERAGING FOR MARTINGALES. Studia Scientiarum Mathematicarum Hungarica, Vol. 37, Issue. 1-2, p. 21.


    Vronskii, M. A. 2000. Refinement of the almost sure central limit theorem for associated processes. Mathematical Notes, Vol. 68, Issue. 4, p. 444.


    Вронский, М А and Vronskii, M A 2000. Уточнение сильной версии центральной предельной теоремы для ассоциированных процессов. Математические заметки, Vol. 68, Issue. 4, p. 513.


    Berkes, István and Horváth, Lajos 1998. Limit Theorems for Logarithmic Averages of Random Vectors. Mathematische Nachrichten, Vol. 195, Issue. 1, p. 5.


    Berkes, I. 1998. Asymptotic Methods in Probability and Statistics.


    Berkes, István Horváth, Lajos and Khoshnevisan, Davar 1998. Logarithmic averages of stable random variables are asymptotically normal. Stochastic Processes and their Applications, Vol. 77, Issue. 1, p. 35.


    Csáki, E. and Földes, A. 1998. Asymptotic Methods in Probability and Statistics.


    Fahrner, I. and Stadtmüller, U. 1998. On almost sure max-limit theorems. Statistics & Probability Letters, Vol. 37, Issue. 3, p. 229.


    Horvath, Lajos and Khoshnevisan, Davar 1995. Weight functions and pathwise local central limit theorems. Stochastic Processes and their Applications, Vol. 59, Issue. 1, p. 105.


    Hurelbaatar, G. 1995. A strong approximation for logarithmic averages of partial sums of random variables. Periodica Mathematica Hungarica, Vol. 31, Issue. 3, p. 189.


    ×
  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 112, Issue 1
  • July 1992, pp. 195-205

Invariance principles for logarithmic averages

  • Miklós Csörgő (a1) and Lajos Horváth (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004100070870
  • Published online: 24 October 2008
Abstract
Abstract

We obtain weak and strong Gaussian approximations for logarithmic averages of indicators of normalized partial sums. The proofs are based on invariance principles for integrals of an Ornstein–Uhlenbeck process and on strong approximations of normalized partial sums by Orstein–Uhlenbeck processes.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2]P. J. Bickel and M. J. Wichura . Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 (1971), 16561670.

[4]N. H. Bingham and R. A. Doney . On higher-dimensional analogues of the arc-sine law. J. Appl. Probab. 25 (1988), 120131.

[6]G. A. Brosamler . The asymptotic behaviour of certain additive functionals of Brownian motion. Invent. Math. 20 (1973), 8796.

[11]U. Einmahl . Strong invariance principles for partial sums of independent random vectors. Ann. Probab. 15 (1987), 14191440.

[14]J. Komlós , P. Major and G. Tusnády . An approximation of partial sums of independent RVs and the sample DF, I. Z. Wahrsch. Verw. Gebiete 32 (1975), 111131.

[15]J. Komlós , P. Major and G. Tusnády . An approximation of partial sums of independent RVs and the sample DF, II. Z. Wahrsch. Verw. Gebiete 34 (1976), 3358.

[16]M. T. Lacey and W. Philipp . A note on the almost sure central limit theorem. Statist. Probab. Lett. 9 (1990), 201205.

[20]P. Révész . Random Walk in Random and Non-Random Environments (World Scientific Publishing Co., 1990).

[21]P. Schatte . On strong versions of the central limit theorem. Math. Nachr. 137 (1988), 249256.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Erratum