Probability pp 415-473 | Cite as

Stationary (Wide Sense) Random Sequences. L2-Theory

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


According to the definition given in the preceding chapter, a random sequence ξ = (ξ 1, ξ 2,...) is stationary in the strict sense if, for every set B ∈ ℬ(R ) and every n ≥ 1,
$$ P\{ ({\xi _1},{\text{ }}{\xi _2}, \ldots ) \in B\} = P\{ ({\xi _{n + 1}},{\text{ }}{\xi _{n + 2}}, \ldots ) \in B\} $$


Spectral Density Random Sequence Spectral Function Spectral Representation Stationary Sequence 
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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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