A White Noise Theory of Infinite Dimensional Calculus

Abstract

Sections 1-4 are based on those three lectures with somewhat more attention devoted to the space of generalized white noise functionals. What is described here are mostly survey articles, though some state-of-the-art results are added, while Section 5 involves a new approach to the study of Gaussian random fields. This topic is exactly what the author wished to propose at the colloquium. What is going to be presented here is, of course, far from a general theory; however it is his hope that this attempt would be the very first step towards the study of Gaussian random fields using variational calculus. Contents: White noise; Generalized functionals; Rotation group and harmonic analysis; Applications to Physics; Gaussian random fields. Keywords: Statistic processes.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1989
Accession Number
ADA221253

Entities

People

  • Takeyuki Hida

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Calculus
  • Delta Functions
  • Exponential Functions
  • Functional Analysis
  • Gaussian Processes
  • Harmonic Analysis
  • Hilbert Space
  • Integrals
  • Mathematics
  • North Carolina
  • Probability
  • Probability Distributions
  • Random Variables
  • Stochastic Processes
  • Three Dimensional
  • White Noise

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Systems Analysis and Design
  • Technical Research and Report Writing.

Technology Areas

  • Space