Weak convergence to fractional brownian motion and to the rosenblatt process

  • Murad S. Taqqu


Stochastic Process Brownian Motion Probability Theory Mathematical Biology Weak Convergence 
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  1. 1.
    Billingsley, P.: Convergence of Probability Measures. New York: Wiley 1968Google Scholar
  2. 2.
    Davydov, Y.A.: The invariance principle for stationary processes. Theor. Probability Appl. 15, 487–498 (1970)Google Scholar
  3. 3.
    de Haan, L.: On regular variation and its application to the weak convergence of sample extremes. Math. Centre Tracts 32, Math. Centre, Amsterdam (1970)Google Scholar
  4. 4.
    Feller, W.: An Introduction to Probability Theory and its Applications 2. 2nd ed. New York: Wiley 1971Google Scholar
  5. 5.
    Gisselquist, R.: A continuum of collision process limit theorems. Ann. Probability 1, 231–239 (1973)Google Scholar
  6. 6.
    Lamperti, J.: Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104, 62–78 (1962)Google Scholar
  7. 7.
    Lukacs, E.: Characteristic Functions. 2nd ed. New York: Hafner 1970Google Scholar
  8. 8.
    Mandelbrot, B.: Limit theorems on the self-normalized range for weakly and strongly dependent processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 31, 271–285 (1975)Google Scholar
  9. 9.
    Mandelbrot, B.: Statistical methodology for non-periodic cycles: from the covariance to R/S analysis. Ann. Econ. and Social Measurement 1, 259–290 (1972)Google Scholar
  10. 10.
    Mandelbrot, B., McCamy, K.: On the secular pole motion and the Chandler wobble. Geophys. J. Roy. Astron. Soc. 21, 217–232 (1970)Google Scholar
  11. 11.
    Mandelbrot, B., van Ness, J.W.: Fractional Brownian motion, fractional noises and applications. SIAM Rev. 10, 422–437 (1968)Google Scholar
  12. 12.
    Mandelbrot, B., Wallis, J.R.: Noah, Joseph and Operational hydrology. Water Resources Research 4, 909–918 (1968)Google Scholar
  13. 13.
    Mandelbrot, B., Wallis, J.R.: Robustness of the rescaled range and the measurement of the long run statistical dependence. Water Resources Research 5, 967–988 (1969)Google Scholar
  14. 14.
    Rosenblatt, M.: Independence and dependence. Proc. 4th Berkeley Sympos. Math. Statist. Probab. pp. 411–443. Berkeley: Univ. Calif. Press 1961Google Scholar
  15. 15.
    Rozanov, Y.A.: Stationary Random Processes. San Francisco: Holden-Day 1967Google Scholar
  16. 16.
    Spitzer, F.: Uniform motion with elastic collision of an infinite particle system. J. Math. Mech. 18, 973–989 (1969)Google Scholar
  17. 17.
    Sun, T.C.: Some further results on central limit theorems for non-linear functions of a normal stationary process. J. Math. Mech. 14, 71–85 (1965)Google Scholar
  18. 18.
    Taqqu, M.: Note on evaluations of R/S for fractional noises and geophysical records. Water Resources Research 6, 349–350 (1970)Google Scholar
  19. 19.
    Taqqu, M.: Limit theorems for sums of strongly dependent random variables. Ph.D. thesis, Columbia Univ. (1972)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Murad S. Taqqu
    • 1
  1. 1.Department of Operations ResearchUpson Hall Cornell UniversityIthacaUSA

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