A nonergodic version of Gordin's CLT for integrable stationary processes

Dalibor Volný

Commentationes Mathematicae Universitatis Carolinae (1987)

  • Volume: 028, Issue: 3, page 413-419
  • ISSN: 0010-2628

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Volný, Dalibor. "A nonergodic version of Gordin's CLT for integrable stationary processes." Commentationes Mathematicae Universitatis Carolinae 028.3 (1987): 413-419. <http://eudml.org/doc/17555>.

@article{Volný1987,
author = {Volný, Dalibor},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {central limit theorems for stationary processes; Martingale limit theory; ergodic decomposition of an invariant measure},
language = {eng},
number = {3},
pages = {413-419},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A nonergodic version of Gordin's CLT for integrable stationary processes},
url = {http://eudml.org/doc/17555},
volume = {028},
year = {1987},
}

TY - JOUR
AU - Volný, Dalibor
TI - A nonergodic version of Gordin's CLT for integrable stationary processes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1987
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 028
IS - 3
SP - 413
EP - 419
LA - eng
KW - central limit theorems for stationary processes; Martingale limit theory; ergodic decomposition of an invariant measure
UR - http://eudml.org/doc/17555
ER -

References

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  1. P. BILLINGSLEY, Ergodic Theory and Information, Wiley, New York, 1965. (1965) Zbl0141.16702MR0192027
  2. C. G. ESSEEN S. JANSON, On moment conditions for normed sums of independent variables and martingale differences, Stoch. proc. and their appl. 19 (1985), 173-182. (1985) MR0780729
  3. M. I. GORDIN, Abstracts of communications, T.1: A-K, International conference on probability theory, Vilnius, 1973. (1973) 
  4. M. I. GORDIN, The central limit theorem for stationary processes, Soviet Math. Dokl. 10 (1969), 1174-1176. (1969) Zbl0212.50005MR0251785
  5. P. HALL C. C. HEYDE, Martingale Limit Theory and its Applications, Academic Press, New York, 1980. (1980) MR0624435
  6. N. HERRHDORF, Stationary strongly mixing sequences not satisfying the central limit theorem, Ann. Probability 11 (1983), 809-813. (1983) MR0704571
  7. M. LOЀVE, Probability Theory, Van Nostrand, New York, 1955. (1955) MR0203748
  8. J. C. OXTOBY, Ergodic sets, Bulletin of the Amer. Math. Soc. 58 (1952), 116-136. (1952) Zbl0046.11504MR0047262
  9. W. F. STOUT, The Hartman-Wintner law of the iterated logarithm for martingales, Ann. Math. Statist. 41 (1970), 2158-2160. (1970) Zbl0235.60046
  10. D. VOLNÝ, The central limit problem for strictly stationary sequences, Ph.D. thesis 1984, Mathematical Institute, Charles university, Prague (in Czech). (1984) 
  11. D. VOLNÝ, Approximation of stationary processes and the central limit problem, Proceedings of the Japan-USSR Symposium on probability theory, Kyoto (1986). (1986) 
  12. D. VOLNÝ R. YOKOYAMA, On the law of iterated logarithm for martingales, submitted for publication. 

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