Probability pp 415-473 | Cite as

Stationary (Wide Sense) Random Sequences. L²-Theory

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• A. N. Shiryaev

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Part of the Graduate Texts in Mathematics book series (GTM, volume 95)

Abstract

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,

$$ P\{ ({\xi _1},{\text{ }}{\xi _2}, \ldots ) \in B\} = P\{ ({\xi _{n + 1}},{\text{ }}{\xi _{n + 2}}, \ldots ) \in B\} $$

(1)

.

Keywords

Spectral Density Random Sequence Spectral Function Spectral Representation Stationary 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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© Springer Science+Business Media New York 1996

Authors and Affiliations

• A. N. Shiryaev
  • 1

1. 1.Steklov Mathematical InstituteMoscowRussia