Strong Exponential Integrability of Martingales with Increments Bounded by a Sequence of Numbers

  • Jan Rosiński
Conference paper
Part of the Progress in Probability book series (PRPR, volume 47)


A strong exponential bound for the probability tail of a martingale whose increments are uniformly bounded by a sequence of numbers is established. The exponent, which grows to infinity faster than a quadratic polynomial, is a Young function determined by that sequence. The related Orlicz norm of a martingale is estimated, some examples are discussed, and the optimality of the exponent is proven.


Orlicz Space Quadratic Polynomial Probability Tail Exact Evaluation Young Function 
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]
    Gluskin, E. D. and Kwapień, S. Tail and moment estimates for sums of independent random variables with logarithmically concave tails. Stu-dia Math. 114(1995), 303–309.MATHGoogle Scholar
  2. [2]
    Krasnoselsky M. A. and Rutitsky Y. B. Convex functions and Orlicz spaces. Noordhof, 1961.Google Scholar
  3. [3]
    Kwapień, S. and Woyczyński, W. A. Random series and stochastic integrals: single and multiple. Probability and its Applications. Birkhäuser Boston, 1992.CrossRefGoogle Scholar
  4. [4]
    Ledoux, M. and Talagrand, M. Probability in Banach spaces. Isoperimetry and processes. Springer-Verlag, 1991.MATHGoogle Scholar
  5. [5]
    Marcus, M. B. ξ-Radial Processes and Random Fourier Series. Memoirs. Amer. Math. Soc. 368 1987. Amer. Math. Soc., Providence, R.I.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Jan Rosiński
    • 1
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

Personalised recommendations