Abstract
The objective of this paper is to study the optimality for stochastic non cooperative elliptic systems. A distributed control problem for a stochastic elliptic systems with constraints on states and controls is studied. First, the existence and uniqueness of the state process for these systems are proved. The necessary and sufficient conditions of optimality are derived for the Dirichlet and Neumann problems.
Highlights
The objective of this paper is to study the optimality for stochastic non cooperative elliptic systems
Stochastic systems play an important role in mathematical models of phenomena in many fields of science, engineering, finance, biology, epidemiology and economics
They deal with stochastic differential equations (SDEs) [6,16]
Summary
Stochastic systems play an important role in mathematical models of phenomena in many fields of science, engineering, finance, biology, epidemiology and economics. Many researchers have been directed to the studies of optimal control of stochastic systems due to their last importance. They deal with stochastic differential equations (SDEs) [6,16]. Zhou was one of the first scientists to have used stochastic partial differential equations (SPDEs). He developed the necessary conditions of optimality (maximum principle) for a very strictly elliptic second order partial differential equations on a d.
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