Accession Number : AD0716581

Title :   Approximations to and Local Properties of Diffusion with Discontinuous Controls,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Kushner,Harold J.

Report Date : NOV 1970

Pagination or Media Count : 30

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.

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*DIFFERENTIAL EQUATIONS, STOCHASTIC PROCESSES), MEASURE THEORY, NUMERICAL INTEGRATION, MULTIVARIATE ANALYSIS, APPROXIMATION(MATHEMATICS), DIFFERENCE EQUATIONS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE