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 Hamil...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 was such optimal control problems is shown to be a viscosity solution of this equation.展开更多
In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose...In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose proof are based on the technique of local time.展开更多
文摘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 was such optimal control problems is shown to be a viscosity solution of this equation.
基金supported by the National Natural Science Foundation of China (No.12261038, 11671408 and11871484)Natural Science Foundation of Jiangxi Province (No.20232BAB201004, 20212BAB201009)Training Program of Young Talents for academic and technical leaders of major disciplines in Jiangxi Province(No.20204BCJL23057)。
文摘In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose proof are based on the technique of local time.
