Probability pp 404-414 | Cite as

Stationary (Strict Sense) Random Sequences and Ergodic Theory

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


Let (Ω P) be a probability space and \( \xi = \left( {{\xi _1},{\xi _2},...} \right) \) a sequence of random variables or, as we say, a random sequence. Let θ k ξ denote the sequence \(\left( {{\xi _{k + 1}},{\xi _{k + 2}},...} \right) \).


Probability Space Random Sequence Strict Sense Stationary Sequence Dominate Convergence Theorem 
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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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