APPLICATION OF LINEAR STOCHASTIC OPERATOR THEORY

Abstract

In diverse areas of physics and engineering, problems arise which should properly be described by linear differential equations with stochastic coefficients. Methods are developed here for finding integral expressions for the second-order statistics (means, correlation functions and power spectrum) of the dependent variable of an nth order linear stochastic differential equation. These expressions constitute a generalization of the corresponding expressions for linear time-varying systems to linear randomly time-varying systems. The kernels of the integral expressions for the statistical measures of the solution can be interpreted as stochastic Green's functions.

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Document Details

Document Type
Technical Report
Publication Date
Oct 21, 1968
Accession Number
AD0682486

Entities

People

  • L. H. Sibul

Organizations

  • Pennsylvania State University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Science
  • Data Science
  • Differential Equations
  • Electrical Engineering
  • Functional Analysis
  • Gaussian Processes
  • Geometry
  • Information Science
  • Integral Equations
  • Partial Differential Equations
  • Random Variables
  • Real Variables
  • Scattering
  • Stationary Processes
  • Stochastic Processes
  • Surveys
  • Wave Functions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.