Stochastic Differential Equations and Models of Random Processes

Abstract

Let us suppose that we are investigating a system whose state can be adequately specified by n real numbers x1, , x(n). We shall suppose that by some acceptable scientific theory it is predicted that, in the absence of disturbances from outside the system, the xi develop in time in accordance with certain differential equations, x(I) = g(I)0 (t,x), I-1,...,n. If there are disturbances or noises,n(1)(t),...n(r)(t), the underlying theory of such systems will often permit us to conclude that x(I) = g(I)0 (t,x) + sigma (sub p=1) g(I)p (t,x) n(p) (t), I = 1, ..., n, which g(I)p is the sensitivity of the ith coordinate to the pth noise.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD1025454

Entities

People

  • E. J. Mcshane

Organizations

  • University of Virginia

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Coefficients
  • Convergence
  • Differential Equations
  • Equations
  • Hypotheses
  • Integral Equations
  • Integrals
  • Interpolation
  • Intervals
  • Notation
  • Numbers
  • Probability
  • Random Variables
  • Real Numbers
  • Scientific Theories
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.