For the d–dimensional reflecting stochastic differential equations (1) with non-smooth boundary and unbounded domain the existence of a strong solution, (weak solution) is obtained under the conditions that the coefficients are less than linear growth and they are non-Lipschitz, (and the diffusion coefficient is non-degenerate, the drift coefficient is bounded and measurable only). Moreover, the Girsanov theorem and the martingale representation theorem with respect to system (1) are also derived. Then by using the Ekeland lemma and the martingale method the existence, necessary and sufficient conditions for an optimal control and an optimal control are obtained. The results are then applied to solve an optimal control problem for a stochastic population model

Existence of solutions and optimal control for reflecting stochastic differential equations with applications to population control theory

For stochastic differential equations with non-Lipschitz diffusion (degenerated) coeffcients and non-Lipschitz drift coefficients, which absolute value can be very much greater than linear growth, the existence of weak, strong solution is obtained under some rather weak conditions, respectively. Then the existence of an optimal (pathwise) Bang-Bang control for a very much non-linear degenerated stochastic system is derived. The technique used here is the martingale approach, local time method, and comparison theorem.

On weak, strong solutions and pathwise bang-bang control for non-linear degenerated stochastic systems1

Situ Rong

Papers

Non-convex stochastic optimal control and maximum principle

On Strong Solutions and Pathwise Stochastic Bang-Bang Control for a Non-Linear System 1

Strong Solutions and Pathwise Control for Multidimensional Non-Linear Stochastic System with Jumps 1

On Weak, Strong Solutions and Pathwise Bang-Bang Control for Nonlinear Degenerated Stochastic Systems 1