Accession Number:

ADA090537

Title:

Existence of Optimal Controls for Partially Observed Diffusions.

Descriptive Note:

Interim rept.,

Corporate Author:

BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS

Personal Author(s):

• Fleming,Wendell H.
• Pardoux,Etienne

Report Date:

1980-07-01

Pagination or Media Count:

59.0

Abstract:

In this paper we are concerned with the existence of optimal controls for problems of the following kind. The state and observation processes are governed by stochastic differential equations. Instead of allowing only strict-sense controls, we obtain existence of a minimum in a wider class of controls. Our results together with a counterexample of Varadhan strongly suggest that, if there is indeed a general existence theorem for strict sense optimal controls, then standard methods are not adequate to prove it. There is a similar difficult in proving existence of optimal controls with complete observations with singular noise coefficient, if the term complete observations is taken in the strict sense that depends on the past of the Wiener process driving the system. Author

Descriptors:

• *CONTROL THEORY
• STOCHASTIC PROCESSES
• MATRICES(MATHEMATICS)
• CONVERGENCE
• DIFFERENTIAL EQUATIONS
• INTEGRAL EQUATIONS
• SET THEORY
• EQUATIONS OF STATE
• THEOREMS
• DERIVATIVES(MATHEMATICS)
• WEAK CONVERGENCE
• HYPERGEOMETRIC FUNCTIONS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE