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References

  • Aliprantis, Charalambos D.; Border, Kim C. Infinite dimensional analysis. A hitchhiker's guide. Third edition. Springer, Berlin, 2006. xxii+703 pp. ISBN: 978-3-540-32696-0; 3-540-32696-0 MR2378491
  • Araujo, Aloisio; Giné, Evarist. The central limit theorem for real and Banach valued random variables. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York-Chichester-Brisbane, 1980. xiv+233 pp. ISBN: 0-471-05304-X MR0576407
  • Billingsley, Patrick. Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396
  • R. C. Bradley, phIntroduction to strong mixing conditions. Vol. 1, Kendrick Press, Heber City, UT, 2007. MR2325294 (2009f:60002a)
  • Dedecker, Jérôme; Merlevède, Florence. On the almost sure invariance principle for stationary sequences of Hilbert-valued random variables. Dependence in probability, analysis and number theory, 157--175, Kendrick Press, Heber City, UT, 2010. MR2731073
  • Dehling, Herold. Limit theorems for sums of weakly dependent Banach space valued random variables. Z. Wahrsch. Verw. Gebiete 63 (1983), no. 3, 393--432. MR0705631
  • Denker, Manfred. Uniform integrability and the central limit theorem for strongly mixing processes. Dependence in probability and statistics (Oberwolfach, 1985), 269--289, Progr. Probab. Statist., 11, Birkhäuser Boston, Boston, MA, 1986. MR0899993
  • Doob, J. L. Stochastic processes. John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. viii+654 pp. MR0058896
  • Doukhan, Paul; Massart, Pascal; Rio, Emmanuel. The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 30 (1994), no. 1, 63--82. MR1262892
  • Giraudo, Davide; Volný, Dalibor. A strictly stationary $\beta$-mixing process satisfying the central limit theorem but not the weak invariance principle. Stochastic Process. Appl. 124 (2014), no. 11, 3769--3781. MR3249354
  • Ledoux, Michel; Talagrand, Michel. Probability in Banach spaces. Isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 23. Springer-Verlag, Berlin, 1991. xii+480 pp. ISBN: 3-540-52013-9 MR1102015
  • Merlevède, Florence; Peligrad, Magda. On the weak invariance principle for stationary sequences under projective criteria. J. Theoret. Probab. 19 (2006), no. 3, 647--689. MR2280514
  • Merlevède, Florence; Peligrad, Magda; Utev, Sergey. Sharp conditions for the CLT of linear processes in a Hilbert space. J. Theoret. Probab. 10 (1997), no. 3, 681--693. MR1468399
  • Mori, Toshio; Yoshihara, Ken-ichi. A note on the central limit theorem for stationary strong-mixing sequences. Yokohama Math. J. 34 (1986), no. 1-2, 143--146. MR0886062
  • Politis, Dimitris N.; Romano, Joseph P. Limit theorems for weakly dependent Hilbert space valued random variables with application to the stationary bootstrap. Statist. Sinica 4 (1994), no. 2, 461--476. MR1309424
  • Rio, Emmanuel. Covariance inequalities for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 29 (1993), no. 4, 587--597. MR1251142
  • Rio, Emmanuel. Théorie asymptotique des processus aléatoires faiblement dépendants. (French) [Asymptotic theory of weakly dependent random processes] Mathématiques & Applications (Berlin) [Mathematics & Applications], 31. Springer-Verlag, Berlin, 2000. x+169 pp. ISBN: 3-540-65979-X MR2117923
  • Rosenblatt, M. A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. U. S. A. 42 (1956), 43--47. MR0074711
  • Rosenthal, Haskell P. On the subspaces of $L^{p}$ $(p>2)$ spanned by sequences of independent random variables. Israel J. Math. 8 1970 273--303. MR0271721
  • Tone, Cristina. Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition. ALEA Lat. Am. J. Probab. Math. Stat. 8 (2011), 77--94. MR2754401
  • Volkonskiĭ, V. A.; Rozanov, Yu. A. Some limit theorems for random functions. I. (Russian) Teor. Veroyatnost. i Primenen 4 1959 186--207. MR0105741
  • Volný, Dalibor. Approximation of stationary processes and the central limit problem. Probability theory and mathematical statistics (Kyoto, 1986), 532--540, Lecture Notes in Math., 1299, Springer, Berlin, 1988. MR0936028
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