关于带跳的反射扩散过程的随机最优控制问题

A Note on Stochastic Optimal Control of Reflected Diffusions With Jumps

研究一类半空间上带泊松跳的反射扩散过程的随机最优控制问题· 得到关于这一控制问题的非线性Nisio半群 ,和联系这一半群的带Neumann边界条件的哈密顿·雅可比·贝尔曼方程· 讨论这一类方程的粘性解的存在唯一性等问题· 证明该控制问题中的价值函数是这一方程的一个粘性解·

Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half_space are considered. The nonlinear Nisio's semigroup for such optimal control problems was constructed. A Hamilton_Jacobi_Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function in such optimal control problems is shown to be a viscosity solution of this equation.