Approximations to and Local Properties of Diffusion with Discontinuous Controls,

Abstract

The stochastic differential (Ito) equation (1), dx = f(x,t,u(x,t))dt + sigma(x,t)dz, where z sub t is a Wiener process, is a common model of a variety of stochastic control systems. Recently, in a paper by Rishel, a transformation of Girsanov was applied to construct a process of the form (1) where u is allowed to be merely bounded and measurable, and proved some theorems concerning the relationship between the formal dynamic programming equation for the cost, and the optimal control. Several questions remain open for the constructed papers by Rishel and Girsanov. As u is not necessarily uniformly Lipschitz, the question of uniqueness remains, and is discussed in this report.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1970
Accession Number
AD0716581

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computer Programming
  • Control Systems
  • Diffusion
  • Dynamic Programming
  • Equations
  • Mathematics
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.