SOME OBSERVATIONS ON MEASURABLE PROPERTIES OF RANDOM PROCESSES AND FIELDS. I,

Abstract

A number of useful, measurable properties of random processes and random fields are de,ined and discussed, and it is shown how these results may be applied to observations necessarily finite in time and in space. Time and space stationarity and ergodicity are considered, as are the definition and construction of hierarchies of probability distribution (densities) defining these stochastic processes and fields. The notion of the intensity spectrum in one or more dimensions is introduced, along with extended versions of the Wiener-Khintchine theorem relating the spectrum to the covariance functions. Cross- and auto-spectral densities are also briefly treated. Some tests of practical stationarity and homogeneity are suggested for finite data sets and single representations, from which approximately statistical (or regular) properties of the ensemble as a whole may be deduced. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 16, 1964
Accession Number
AD0434120

Entities

People

  • David Middleton

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Construction
  • Covariance
  • Data Sets
  • Ergodic Processes
  • Hierarchies
  • Homogeneity
  • Intensity
  • Mathematics
  • Observation
  • Probability
  • Probability Distributions
  • Random Variables
  • Spectra
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space