On the Distribution of the Integrated Square of the Ornstein-Uhlenbeck Process

Abstract

Using functional integral methods, one calculates the Laplace transform of the square of the Ornstein-Uhlenbeck process X(t) integrated over 0 < or = t < or = T, invert this transform via infinite series, and study the asymptotic behavior as T approaches infinity of the density and distribution functions, as well as these functions conditioned on the event X(T) = 0. We find that the approximation by an inverse Gaussian distribution, introduced earlier by Grenander, Pollak, and Slepian, is asymptotically correct (to within a constant factor) in the conditional case, but in the unconditional case.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA207253

Entities

People

  • Thad Dankel Jr.

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Availability
  • Classification
  • Covariance
  • Data Science
  • Distribution Functions
  • Gaussian Distributions
  • Information Science
  • North Carolina
  • Probability
  • Probability Density Functions
  • Probability Distribution Functions
  • Probability Distributions
  • Real Numbers
  • Security
  • Statistics
  • Surveys
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Statistical inference.