DING Deng. A Note on Stochastic Optimal Control of Reflected Diffusions With Jumps[J]. Applied Mathematics and Mechanics, 2000, 21(9): 973-983.
Citation: DING Deng. A Note on Stochastic Optimal Control of Reflected Diffusions With Jumps[J]. Applied Mathematics and Mechanics, 2000, 21(9): 973-983.

A Note on Stochastic Optimal Control of Reflected Diffusions With Jumps

  • Received Date: 1999-04-06
  • Rev Recd Date: 2000-04-16
  • Publish Date: 2000-09-15
  • Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered.The nonlinear Nisio.s semigro up for such optimal control problems was constructed.A Hamilton-Jaco bi-Bellman equation with the Ne umann boundary condition associated with this semigroup was o btained.Then,visco sity 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.
  • loading
  • [1]
    Lions P L. Optimal control of reflected diffusion processes[J]. Lect Notes in Control and Inf Sci,1983,61:157-163.
    [2]
    Menaldi J L, Robin M. construction and control of reflected diffusion with jumps[J]. Lect Notes in Control and Inf Sci,1983,69:309-322.
    [3]
    Maurel M C, Karoui N E, Marchal B. Reflexiom discontinue et systemes stochastiques[J]. Ann Probab,1980,8(3):1047-1067.
    [4]
    丁灯. 关于带跳反射扩散过程的下鞅问题及其应用[J]. 中山大学学报(自然科学版),1995,34(2):7-13.
    [5]
    Lions P L, Menaldi J L. Optimal control of stochastic integrals and Hamilton-Jacobi-Bellman equations, Parts 1 and 2[J]. SIAM J Control Optim,1980,20(1):58-95.
    [6]
    Krylov N V. Controlled Diffusion Processes[M]. Berlin: Springer,1985.
    [7]
    Nisio M. Lectures on Stochastic Control Theory[M]. Macmillan India Limited,1981.
    [8]
    Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes[M]. Tokyo: North-Holland Publishing Compang,1981.
    [9]
    Krylov N V, Pragarauskas H. On the Bellman equations for uniformly non-degenerated general stochastic processes[J]. Liet Matem Rink,1980,20(1):85-95.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2606) PDF downloads(732) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return