On the functional form of Lévy's modulus of continuity for Brownian motion

  • A. de Acosta
Article

Keywords

Stochastic Process Brownian Motion Probability Theory Functional Form Mathematical Biology 

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References

  1. 1.
    de Acosta, A.: Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm. Ann. Probab. 11, 78–101 (1983)Google Scholar
  2. 2.
    de Acosta, A., Kuelbs, J.: Limit theorems for moving averages of independent random vectors. Z. Wahrscheinlichkeitstheor. Verw. Geb. 64, 67–123 (1983)Google Scholar
  3. 3.
    Azencott, R.: Grandes déviations et applications. Lecture Notes in Mathematics 774. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  4. 4.
    Borell, C.: The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30, 207–216 (1975)Google Scholar
  5. 5.
    Carmona, R.: Module de continuité uniforme des mouvements browniens à valeurs dans un espace de Banach. C.R. Acad. Sci., Paris, Ser. A 281, 659–662 (1975)Google Scholar
  6. 6.
    Csáki, E.: A relation between Chung's and Strassen's laws of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 287–301 (1980)Google Scholar
  7. 7.
    Csörgő, M., Révész, P.: How small are the increments of a Wiener process? Stochastic Processes Appl. 8, 119–129 (1979)Google Scholar
  8. 8.
    Csörgő, M., Révész, P.: How big are the increments of a Wiener process? Ann. Probab. 7, 731–733 (1979)Google Scholar
  9. 9.
    Csörgő, M., Révész, P.: Strong approximations in probability and statistics. New York: Academic Press 1981Google Scholar
  10. 10.
    Dugundji, J.: Topology. Boston: Allyn and Bacon 1966Google Scholar
  11. 11.
    Lévy, P.: Processus stochastiques et mouvement Brownien. Paris: Gauthier-Villars 1948Google Scholar
  12. 12.
    McKean, H.: Stochastic integrals. New York: Academic Press, 1969Google Scholar
  13. 13.
    Mueller, C.: A unification of Strassen's law and Lévy's modulus of continuity. Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 163–179 (1981)Google Scholar
  14. 14.
    Révész, P.: A generalization of Strassen's functional law of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb. 50, 257–264 (1979)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • A. de Acosta
    • 1
  1. 1.Department of Mathematics and StatisticsCase Western Reserve UniversityClevelandUSA

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