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Martingales

  • Yuan Shih Chow
  • Henry Teicher
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

An introduction to martingales appeared in Section 7.4, where convergence theorems for submartingales {S n , ℱ n , n ≥ 1} (relating to differentiation theory) were discussed. Here, emphasis will fall upon convergence theorems for martingales {S -n , ℱ -n , n ≤ -1} (relating to ergodic theorems). In demarcating the two cases, it is natural to refer to a martingale {S n , ℱ n , n ≥ 1} as an upward martingale and to allude to a martingale {S -n , ℱ -n , n ≤ -1} when written {S n , ℱ n , n ≥ 1} as a downward or reverse martingale. Martingale and stochastic inequalities will also be dealt with.

Keywords

Nondecreasing Function Martingale Difference Uniform Integrability Nonnegative Measurable Function Stochastic Sequence 
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.

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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Yuan Shih Chow
    • 1
  • Henry Teicher
    • 2
  1. 1.Department of Mathematical StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsRutgers UniversityNew BrunswickUSA

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