Skip to main content

Part of the book series: Springer Series in Statistics ((SSS))

  • 791 Accesses

Abstract

1The exact meaning of this statement is related to some refined mathematical considerations which are, in fact, closely associated with the way a random function arises, usually in an actual physical context. As already emphasized in the Introduction, in order to apply probabilistic methods, we must have an experiment which can be repeated many times under similar conditions and which can lead to different outcomes. The set Ω of all possible outcomes ω* of such an experiment (the set of so-called elementary events) plays a basic role in Kolmogorov’s axiomatic formulation of probability theory (see, e.g., Kolmogorov, 1956; Cramér, 1962; Shiryaev (1980); or any other modern advanced text on probability). A random variable X is a quantity which takes different numerical values for different outcomes of an experiment. In other words, a random variable is a numerical function of the point ω* of the set Ω. Therefore, it would be more accurate to write X*) instead of X. (This was not done anywhere above, since in probability theory, the dependence of random variables on an elementary event ω* is traditionally suppressed.) From this point of view, a random function X(t) on T should be defined as a function X(t*) of two variables t and ω*.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Yaglom, A.M. (1987). Chapter 1. In: Correlation Theory of Stationary and Related Random Functions. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4628-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4628-2_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9090-2

  • Online ISBN: 978-1-4612-4628-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics