Multiple stable integrals appearing in weak limits

  • Jerzy Szulga
Part of the Progress in Probabilty book series (PRPR, volume 25)


Limit laws of certain finite multilinear random forms coincide with distributions of stable multiple integrals.


Random Measure Weak Limit Empirical Measure Multilinear Form Finite Dimensional Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Dehling, D., Denker, M., Woyczyński, W. A. (1988). Resampling U-statistics using p-stable laws. Preprint (to appear in J. Mult. Anal.)Google Scholar
  2. [2]
    Dehling, H., Denker, M., Philipp, W. (1984) Invariance principles for sums of Banach space valued random elements and empirical processes. Z. Wahr. verw. Geb. 62 509–552.MathSciNetGoogle Scholar
  3. [3]
    Engel, D. D. (1982). The multiple stochastic integral. Mem. Amer. Math. Soc. 38 # 265.MathSciNetGoogle Scholar
  4. [4]
    Feller W. (1971). An Introduction to Probability Theory and its Applications. Vol.2, 2nd ed., Wiley, New York.Google Scholar
  5. [5]
    Filippova, A.A. (1962). Mises’ theorem on asymtotic behavior of functionals of empirical distribution functions and its statistical applications. Theory Prob. Appl. 7 24–57.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Itô, K. (1956). Spectral type of shift transformations of differential processes with stationary increments, Trans. Amer. Math. Soc. 81 253–263.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Kallenberg, O. (1989). Some uses of point processes in miltiple stochastic integration. Tech. Report #269, UNC, Chapel Hill.Google Scholar
  8. [8]
    Kallenberg, O., Szulga (1989). Multiple stochastic integrals with respect to Poisson and Levy processes, to appear in Probab. Th. Rel. Fields.Google Scholar
  9. [9]
    Krakowiak, W., Szulga, J. (1988). Hypercontraction principle and random multilinear forms. Probab. Th. rel. Fields 77 325–342.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Krakowiak, W., Szulga, J. (1988). A multiple stochastic integral with respect to a strictly p-stable random measure. Ann. Probab. 16 764–777.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    Kwapien, S., Szulga, J. (1989) Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces. to appear in Ann. Probab.Google Scholar
  12. [12]
    Rosinski, J., Woyczynski, W. A. (1986). On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals. Ann. Probab. 14 271–286.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Surgailis, D. (1985). On the multiple stable integral. Z. Wahrschein. verw. Gebiete 70 621–632.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    Zolotarev, V.M. (1986). One dimensional stable distributions. Transi. of Math. Monographs, Amer. Math. Soc, Providence, Rhode Island.MATHGoogle Scholar
  15. [15]
    Zolotarev, V.M., (1983). Probability metrics. Theory Probab. Appl. 28 278–302.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Jerzy Szulga
    • 1
  1. 1.Mathematics ACAAuburn UniversityAuburnUSA

Personalised recommendations