Probability pp 474-563 | Cite as

Sequences of Random Variables That Form Martingales

  • A. N. Shiryaev
Part of the Graduate Texts in Mathematics book series (GTM, volume 95)


The study of the dependence of random variables arises in various ways in probability theory. In the theory of stationary (wide sense) random sequences, the basic indicator of dependence is the covariance function, and the inferences made in this theory are determined by the properties of that function. In the theory of Markov chains (§12.of Chapter I; Chapter VIII) the basic dependence is supplied by the transition function, which completely determines the development of the random variables involved in Markov dependence.


Independent Random Variable Absolute Continuity Local Martingale Dependent Random Variable Martingale Property 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • A. N. Shiryaev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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