Jump-Diffusion Approximations for Ordinary Differential Equations with Wide-Band Random Right Hand Sides,

Abstract

Let Y(*) be a stationary mixing process and J superscript epsilon (*) an approximation to a random impulsive process. Kurtz's results on approximation of a general semigroup by a Markov semigroup are used to prove (weak and a similar type of) convergence of the solutions to (1.1) and to jumping diffusions. Previous results are generalized in various ways. The case of unbounded y(*) is also treated as is the combined jump-diffusion case. Also, a limit theorem for an integral with respect to approximate white noise in terms of an Ito integral is given. The method has the advantages of generality and relative ease of use. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1978
Accession Number
ADA061950

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analytic Functions
  • Applied Mathematics
  • Brownian Motion
  • Coefficients
  • Convergence
  • Differential Equations
  • Equations
  • Integrals
  • Markov Processes
  • Mixing
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Sequences
  • Stationary Processes
  • Truncation
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Mathematical Modeling and Probability Theory.