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Rates of growth for banach space valued independent increment processes

Part of the Lecture Notes in Mathematics book series (LNM,volume 709)

Keywords

  • Brownian Motion
  • Sample Path
  • Stable Process
  • Empirical Process
  • Independent Increment

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Bibliography

  1. Anderson, T. W. and Darling, D.A. (1952), Asymptotic theory of certain "goodness of fit" criteria based on stochastic processes, Ann. Math. Stat. Vol. 23, pp. 193–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Berkes, I. and Philipp, W. (1977), An almost sure invariance principle for the empirical distribution function of mixing random variables, Z. Wahr. Verw. Gebiete, Vol. 41, pp. 115–137.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Billingsley, P. (1968), Convergence of Probability Measures, J. Wiley & Sons, New York.

    MATH  Google Scholar 

  4. Bojanic, R. and Seneta, E. (1971), Slowly varying functions and asymptotic relations, J. Math. Anal. Appl., Vol. 34, pp. 302–315.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Breiman, L. (1968), Probability, Addison Wesley, Publ. Co., Reading, Massachusetts.

    MATH  Google Scholar 

  6. Cameron, R. H. and Martin, W. T. (1944), The Wiener measure of Hilbert neighborhoods in the space of real continuous functions, J. of Math. and Physics, Vol. 23, pp. 195–209.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Chung, K. L. (1948), On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc., Vol. 64, pp. 205–233.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. De Acosta, Alejandro (1975), Stable Measures and Seminorms, Annals of Prob., Vol. 3, pp. 865–875.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Dudley, R. M., Hoffman-Jørgensen, J. and Shepp, L. A. (1977), On the lower tail of Gaussian seminorms, Aarhus Universitet Preprint series.

    Google Scholar 

  10. Dudley, R. M. and Kanter, M. (1974), Zero-One laws for Stable Measures, Proc. American Math. Soc., Vol. 25, pp. 245–252.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Dvoretsky, A. and Erdös, P. (1951), Some problems on random walk in space, Proc. Second Berkeley Sym. Math., Statistics, and Prob., pp. 353–367.

    Google Scholar 

  12. Erickson, K. B. (1978), Rates of escape of infinite dimensional Brownian motion, Submitted for publication.

    Google Scholar 

  13. Feller, W. (1970), An introduction to probability theory and its applications, Vol. 2, second edition, J. Wiley & Sons, New York.

    MATH  Google Scholar 

  14. Femique, X. (1970), Integrabilité des vecteurs Gaussiens, C. R. Acad. Sci. Paris Ser. A, Vol. 270, pp. 1698–1699.

    MathSciNet  MATH  Google Scholar 

  15. Gihman, I. I. and Skorohod, A. V. (1974), The Theory of Stochastic Processes I, Springer-Verlag, Berlin.

    CrossRef  MATH  Google Scholar 

  16. Hildebrand, F. B., Advanced Calculus for Applications, second edition, Prentice Hall Inc., Englewood Cliffs, New Jersey.

    Google Scholar 

  17. Kiefer, J. (1972), Skorohod embedding of multivariate random variables and the sample D. F., Z. Wahr. Verw. Gebiete, Vol. 24, pp. 1–35.

    CrossRef  MATH  Google Scholar 

  18. Kuelbs, J. (1973), The invariance principle for Banach space valued random variables, J. Multivariate Analysis, Vol. 3, pp. 161–172.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____ (1975), Sample path behavior for Brownian motion in Banach spaces, Ann. o f Prob., Vol. 3, pp. 247–261.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Seneta, E. (1976), Regularly varying functions, Lecture Notes in Mathematics, Vol. 508, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  21. Takeuchi, J. (1964), On the sample paths of the symmetric stable processes in spaces, J. Math. Soc. Japan, Vol. 16, pp. 109–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1979 Springer-Verlag

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Kuelbs, J. (1979). Rates of growth for banach space valued independent increment processes. In: Beck, A. (eds) Probability in Banach Spaces II. Lecture Notes in Mathematics, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071956

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  • DOI: https://doi.org/10.1007/BFb0071956

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  • Print ISBN: 978-3-540-09242-1

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