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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)

Abstract

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.

Keywords

Orlicz Space Quadratic Polynomial Probability Tail Exact Evaluation Young Function 
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References

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

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

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