PARTIAL DIFFERENTIAL EQUATIONS FOR DENSITIES OF RANDOM PROCESSES,

Abstract

The Fokker-Planck-Kolmogorov (FPK) equation appears to be of wider applicability than is commonly realized. It is proved that the density functions for a wider class of vector random processes than just the Markov processes satisfy the FPK equation. Furthermore, an analogous derivation will yield a different partial differential equation applicable to multivariate densities for scalar random processes. The central technique is the evaluation of time derivatives of the characteristic function for the random variables of interest by two different methods; the comparison of the two different expressions for the time derivatives then yields the desired partial differential equations. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 04, 1964
Accession Number
AD0604005

Entities

People

  • Terrence Fine

Organizations

  • Harvard University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Fokker Planck Equations
  • Markov Processes
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Random Variables
  • Real Variables

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.