A Martingale Method for the Convergence of a Sequence of Processes to a Jump-Diffusion Process

Abstract

A convenient method for proving weak convergence of a sequence of non-Markovian processes x(epsilon) (.) to a jump-diffusion process is proved. Basically, it is shown that the limit solves the martingale problem of Strook and Varadhan. The proofs are relatively simple, and the conditions apparently weaker than required by other current methods (in particular, for limit theorems for a sequence of ordinary differential equations with random right hand sides). In order to illustrate the relative ease of applicability in many cases, a simpler proof of a known result on averaging is given.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1979
Accession Number
ADA080083

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Arc Lamps
  • Boundary Value Problems
  • Compressors
  • Differential Equations
  • Electrical Engineering
  • Electrodes
  • Engineering
  • High Pressure
  • Impedance
  • Lamps
  • Measurement
  • Monitoring
  • Power Distribution
  • Power Levels
  • Temperature Gradients
  • Transmission Lines
  • Waveguides

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.