Hamilton-Jacobi-Bellman Equations and the Optimal Control of Stochastic Systems
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چکیده
In many applications (engineering, management, economy) one is led to control problems for stochastic systems : more precisely the state of the system is assumed to be described by the solution of stochastic differential equations and the control enters the coefficients of the equation. Using the dynamic programming principle E. Bellman [6] explained why, at least heuristically, the optimal cost function (or value function) should satisfy a certain partial differential equation called the Hamilton-JacobiBellman equation (HJB in short), which is of the following form
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