Existence of Optimal Stochastic Controls (I). Convergence of the Finite Difference Approximations of a Discounted Problem for a Diffusion.

Abstract

In part one the author gives a fairly general method for proving the existence of an optimal control for a large class of stochastic differential equation models. In part two, it is shown that the solutions to finite difference approximations to the partial differential equation converge to C(x) as the difference interval goes to zero, whether or not the derivatives actually exist. The result generalizes previous results for similar problems, and the techniques can be applied to a number of related problems. (Modified author abstract)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1974
Accession Number
AD0778767

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Convergence
  • Differential Equations
  • Diffusion
  • Equations
  • Fokker Planck Equations
  • Intervals
  • Mathematical Analysis
  • Partial Differential Equations
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.