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Central limit theorems for dependent random vectors in Banach spaces

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Martingale Theory in Harmonic Analysis and Banach Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 939))

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References

  1. A. de Acosta, Existence and convergence of probability measures in Banach spaces, Trans. Amer. Math. Soc. 152 (1970), 273–298.

    MathSciNet  MATH  Google Scholar 

  2. A. de Acosta, A. Araujo and E. GinĂ©, On Poisson measures, Gaussian measures and the central limit theorem in Banach spaces, Advances in Probability 5 (1978), 1–68, Dekker, New York.

    Google Scholar 

  3. P. Assouad, Espaces p-lisses, rearrangements, Sem. Maurey-Schwartz 1974/75, Exp. XVI.

    Google Scholar 

  4. B. M. Brown, Martingale central limit theorems, Ann. Math. Stat. 42 (1971), 59–66.

    Article  MathSciNet  MATH  Google Scholar 

  5. B. M. Brown and G. K. Eagleson, Martingale convergence to infinitely divisible laws with finite variances, Trans. Amer. Math. Soc. 162 (1971), 449–453.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. L. Burkholder, Distribution function inequalities for martingales, Ann. Prob. 1 (1973), 19–42.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. L. Burkholder, A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Prob. 9 (1981), 997–1011.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. M. Day, Normed Linear Spaces, Third Edition, Springer-Verlag, Berlin-Heidelberg-New York, 1973.

    Book  MATH  Google Scholar 

  9. A. Dvoretzky, The central limit theorems for dependent random variables, Proc. of the Int. Congress of Math., Nice, 1970.

    Google Scholar 

  10. A. Dvoretzky, Asymptotic normality for sums of dependent random variables, Proc. 6th Berkeley Symp. Math. Stat. Prob., Univ. California (1971), 513–535.

    Google Scholar 

  11. D. J. H. Garling, Functional central limit theorems in Banach spaces, Ann. Prob. 4 (1976), 600–611.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Jakubowski, On limit theorems for sums of dependent Hilbert space valued random variables, Lecture Notes in Statistics 2, (1980), 178–187.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. C. James, Non-relfexive spaces of type 2, Israel J. Math. 30 (1978) 1–13.

    Article  MathSciNet  Google Scholar 

  14. A. KƂopotowski, Limit theorems for sums of dependent random vectors in R d, Disert. Math 151 (1977), 1–55.

    MathSciNet  MATH  Google Scholar 

  15. K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.

    Book  MATH  Google Scholar 

  16. G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326–350.

    Article  MathSciNet  MATH  Google Scholar 

  17. W. F. Stout, Almost Sure Convergence, Academic Press, New York, 1974.

    MATH  Google Scholar 

  18. J. Szulga, Three series theorem for martingales in Banach spaces, Bull. Acad. Polon. Sci. 25 (1977), 175–180.

    MathSciNet  MATH  Google Scholar 

  19. W. A. WoyczƄski, Laws of large numbers for vector valued martingales, Bull. Acad. Polon. Sci. 23 (1975), 1199–1201.

    MathSciNet  Google Scholar 

  20. W. A. WoyczyƄski, Weak convergence to a Gaussian measure of martingales in Banach spaces, Symp. Math. 21 (1977), 319–331.

    MathSciNet  MATH  Google Scholar 

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Jia-Arng Chao Wojbor A. WoyczyƄski

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© 1982 Springer-Verlag

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RosiƄski, J. (1982). Central limit theorems for dependent random vectors in Banach spaces. In: Chao, JA., WoyczyƄski, W.A. (eds) Martingale Theory in Harmonic Analysis and Banach Spaces. Lecture Notes in Mathematics, vol 939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096267

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  • DOI: https://doi.org/10.1007/BFb0096267

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  • Print ISBN: 978-3-540-11569-4

  • Online ISBN: 978-3-540-39284-2

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