Lithuanian Mathematical Journal

, Volume 22, Issue 3, pp 327–340 | Cite as

Zones of attraction of self-similar multiple integrals

  • D. Surgailis
Article

Keywords

Multiple Integral 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    R. Bentkus and Ya. Rudzkis, “Exponential estimates of the distribution of random variables,” Liet. Mat. Rinkinys,20, No. 1, 15–30 (1980).Google Scholar
  2. 2.
    B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley (1968).Google Scholar
  3. 3.
    V. V. Gorodetskii, “Convergence to semistable Gaussian processes,” Teor. Veroyatn. Primen.,22, No. 3, 513–522 (1977).Google Scholar
  4. 4.
    V. V. Gorodetskii, “Estimate of the rate of convergence in limit theorems for random processes,” Author's Abstract of Candidate's Dissertation, Leningrad (1977).Google Scholar
  5. 5.
    Yu. A. Davydov, “Invariance principle for random processes,” Teor. Veroyatn. Primen.,15, No. 3, 498–509 (1979).Google Scholar
  6. 6.
    R. L. Dobrushin, “Self-similarity and the renormalization group of generalized random fields,” in: Multicomponent Random Systems [in Russian], Nauka, Moscow (1978), pp. 179–213.Google Scholar
  7. 7.
    R. L. Dobrushin, “Gaussian and their subordinated self-similar random generalized fields,” Ann. Probab.,7, 1–28 (1979).Google Scholar
  8. 8.
    R. L. Dobrushin and P. Major, “Noncentral limit theorems for nonlinear functionals of Gaussian fields,” Z. Wahr. Verw. Geb.,50, 27–52 (1979).Google Scholar
  9. 9.
    T. Hida, Stationary Stochastic Processes, Princeton Univ. Press (1970).Google Scholar
  10. 10.
    D. Iagolnitzer and B. Souillard, “Random fields and limit theorems,” Ecole Polytechnique, Preprint (1979).Google Scholar
  11. 11.
    K. Ito, “Multiple Wiener integral,” J. Math. Soc. Jpn.,3, 157–164 (1951).Google Scholar
  12. 12.
    I. A. Ibragimov and Yu. V. Linnik, Independent and Stationarily Connected Quantities [in Russian], Nauka, Moscow (1965).Google Scholar
  13. 13.
    H. Kesten and F. Spitzer, “A limit theorem related to a new class of self-similar processes,” Z. Wahr. Verw. Geb.,50, 5–25 (1979).Google Scholar
  14. 14.
    A. N. Kolmogorov, “Wiener spiral and some other interesting curves in Hilbert space,” Dokl. Akad. Nauk SSSR,26, No. 2, 115–118 (1940).Google Scholar
  15. 15.
    J. Lamperti, “Semistable stochastic processes,” Trans. Am. Math. Soc.,104, 62–78 (1962).Google Scholar
  16. 16.
    P. Major, “Multiple Wiener-Ito Integrals,” Lect. Notes Math., Vol. 849, Springer-Verlag (1981).Google Scholar
  17. 17.
    M. Rosenblatt, “Independence and dependence,” in: Proc. Fourth Berkeley Symp. Math. Statist. Probab., Berkeley (1961), pp. 431–443.Google Scholar
  18. 18.
    M. Rosenblatt, “Limit theorems for Fourier transforms of functionals of Gaussian sequences,” Z. Wahr. verw. Geb.,55, 123–132 (1981).Google Scholar
  19. 19.
    Ya. G. Sinai, Theory of Phase Transitions [in Russian], Nauka, Moscow (1980).Google Scholar
  20. 20.
    D. Surgailis, “Convergence of sums of nonlinear functions of moving averages to self-similar processes,” Dokl. Akad. Nauk SSSR,257, No. 1, 51–54 (1981).Google Scholar
  21. 21.
    D. Surgailis, “Linear random fields and those subordinate to them,” Doctoral Dissertation, Vilnius (1981).Google Scholar
  22. 22.
    D. Surgailis, “On infinitely divisible self-similar random fields,” Z. Wahr. Verw. Geb.,80, 453–477 (1981).Google Scholar
  23. 23.
    D. Surgailis, “On L2 and non-L2-multiple stochastic integrals,” in: Proc. Third IFIP Working Conf. Stoch. Diff. Syst., Lecture Notes Control Information Sciences, Vol. 36, Springer (1981), pp. 212–226.Google Scholar
  24. 24.
    M. S. Taqqu, “Self-similar processes and related ultraviolet and infrared catastrophes,” Cornell Univ., Preprint (1979).Google Scholar
  25. 25.
    M. S. Taqqu, “Convergence of integrated processes of arbitrary Hermite rank,” Z. Wahr. Verw. Geb.,50, 53–83 (1979).Google Scholar
  26. 26.
    W. Feller, Introduction to Probability Theory and Its Applications, Wiley (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • D. Surgailis

There are no affiliations available

Personalised recommendations