Multiplicative Stochastic Processes Involving the Time-Derivative of a Markov Process.

Abstract

The characteristic functional of the derivative phi(t) of a Markov process phi(t) and the related multiplicative process sigma(t), which obeys the stochastic differential equation isigma(t) = (A + phi(t)B)sigma(t), have been studied. Exact equations for the marginal characteristic functional and the marginal average of sigma(t) are derived. The first equation is applied to obtain a set of equations for the marginal moments of phi(t) in terms of the prescribed properties of phi(t). It is illustrated by an example how these equations can be solved, and it is shown in general that phi(t) is delta-correlated, with a smooth background. The equation of motion for the marginal average of sigma(t) is solved for various cases, and it is shown how closed-form analytical expressions for the average <sigma(t)> can be obtained. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1986
Accession Number
ADA170649

Entities

People

  • Henk F. Arnoldus
  • Thomas F. George

Organizations

  • University at Buffalo

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Air Force
  • Chemical Engineering
  • Chemistry
  • Differential Equations
  • Fokker Planck Equations
  • Governments
  • Intellectual Property
  • Markov Processes
  • Materials
  • Materials Science
  • Military Research
  • New York
  • Partial Differential Equations
  • Physics
  • Stochastic Processes
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.