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Conditioning and martingales

  • M. M. Rao
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 342)

Abstract

The concept of conditioning, or equivalently conditional expectation, is one of the most fundamental notions in Probability. After some motivation for the concept, we discuss some immediate properties of conditional expectations (and probabilities). Then the regularity of conditional probabilities and some related results are discussed. Next the concept of a martingale, the basic inequalities, and the decompositions of Riesz, Doob (in the discrete case) and Jordan type [for (sub) martingales] are presented. The discrete parameter convergences of martingales, including the Andersen-Jessen theorems, are discussed. Related Complements with some details, are contained as exercises in the last section.

Keywords

Probability Space Conditional Expectation Banach Lattice Vector Measure Orlicz Space 
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 Science+Business Media Dordrecht 1995

Authors and Affiliations

  • M. M. Rao
    • 1
  1. 1.University of CaliforniaRiversideUSA

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