Approche variationnelle du principe stochastique de Pontriagin

Abstract

The subject of this work is the study of stochastic principle of Pontryagin. First, we study the stochastic differential equations specially, the existence and uniqueness of the solution and its general properties Second, we study the existence of an optimal control realizing the infimum of the coast function associated to the problem of ordinary control. After that, we study the relaxed control problem. Finally, we establish the stochastic pontryagin principle for the strong formulation in order to have the necessary conditions of optimality.