留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一般正倒向重随机微分方程的解

朱庆峰 石玉峰 宫献军

朱庆峰, 石玉峰, 宫献军. 一般正倒向重随机微分方程的解[J]. 应用数学和力学, 2009, 30(4): 484-494.
引用本文: 朱庆峰, 石玉峰, 宫献军. 一般正倒向重随机微分方程的解[J]. 应用数学和力学, 2009, 30(4): 484-494.
ZHU Qing-feng, SHI Yu-feng, GONG Xian-jun. Solutions of General Forward-Backward Doubly Stochastic Differential Equations[J]. Applied Mathematics and Mechanics, 2009, 30(4): 484-494.
Citation: ZHU Qing-feng, SHI Yu-feng, GONG Xian-jun. Solutions of General Forward-Backward Doubly Stochastic Differential Equations[J]. Applied Mathematics and Mechanics, 2009, 30(4): 484-494.

一般正倒向重随机微分方程的解

基金项目: 国家自然科学基金资助项目(10771122);山东省自然科学基金资助项目(Y2006A08);国家重点基础研究发展计划(973计划,2007CB814900)
详细信息
    作者简介:

    朱庆峰(1978- ),男,山东泰安人,讲师,硕士(E-mail:zhuqf508@sohu.com);石玉峰,教授(联系人.E-mail:yfshi@sdu.edu.cn).

  • 中图分类号: O211.63;O211.5

Solutions of General Forward-Backward Doubly Stochastic Differential Equations

  • 摘要: 研究了一类正倒向重随机微分方程,其涵盖了以前的包括随机Hamilton系统的很多情况.通过连续性方法,在较弱的单调条件下得到了其解的存在唯一性结果.然后研究了正倒向重随机微分方程的解依赖于参数的连续性和可微性.
  • [1] Pardoux E, Peng S G.Adapted solution of a backward stochastic differential equation[J].Systems Control Letters,1990,14(1):55-61. doi: 10.1016/0167-6911(90)90082-6
    [2] El Karoui N,Peng S G,Quenez M C. Backward stochastic differential equations in finance[J].Mathematical Finance,1997,7(1):1-71. doi: 10.1111/1467-9965.00022
    [3] Ma J,Yong J M.Forward-Backward Stochastic Differential Equations and Their Applications[M]. Lecture Notes in Mathematics,1702,Berlin: Springer,1999.
    [4] Antonelli F. Backward-forward stochastic differential equations[J].The Annals of Applied Probability,1993,3(3):777-793. doi: 10.1214/aoap/1177005363
    [5] Ma J,Protter P,Yong J M. Solving forward-backward stochastic differential equations explicitly—a four step scheme[J].Probab Theory Related Fields,1994,98(2):339-359. doi: 10.1007/BF01192258
    [6] Hu Y,Peng S G. Solution of forward-backward stochastic differential equations[J].Probab Theory Related Fields,1995,103(2):273-283. doi: 10.1007/BF01204218
    [7] Peng S G,Wu Z. Fully coupled forward-backward stochastic differential equations and applications to optimal control[J].SIAM J Control Optim,1999,37(3):825-843. doi: 10.1137/S0363012996313549
    [8] Yong J M. Finding adapted solutions of forward-backward stochastic differential equations—method of continuation[J].Probab Theory Related Fields,1997,107(3):537-572. doi: 10.1007/s004400050098
    [9] Peng S G,Shi Y F. Infinite horizon forward-backward stochastic differential equations[J].Stochastic Processes and Their Applications,2000,85(1):75-92. doi: 10.1016/S0304-4149(99)00066-6
    [10] Peng S G. Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions[J].Stochastic Processes and Their Applications,2000,88(2):259-290. doi: 10.1016/S0304-4149(00)00005-3
    [11] Bismut J M. Conjugate convex functions in optimal stochastic control[J].Journal of Mathematial Analysis and Applications,1973,44(4):384-404. doi: 10.1016/0022-247X(73)90066-8
    [12] Peng S G,Shi Y F. A type of time-symmetric forward-backward stochastic differential equations[J].C R Acad Sci Paris,Ser Ⅰ,2003,336(9): 773-778. doi: 10.1016/S1631-073X(03)00183-3
    [13] Pardoux E,Peng S G. Backward doubly stochastic differential equations and systems of quasilinear parabolic SPDE's[J].Probab Theory Related Fields,1994,98(2):209-227. doi: 10.1007/BF01192514
    [14] Shi Y F. Singularly perturbed boundary value problems[J].Acta Mathematicae Applacatea Sinica,1999,15(4):409-417. doi: 10.1007/BF02684042
    [15] Peng S G. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations[J].Stochastics,1991,37(1/2):61-74.
  • 加载中
计量
  • 文章访问数:  2708
  • HTML全文浏览量:  66
  • PDF下载量:  643
  • 被引次数: 0
出版历程
  • 收稿日期:  2008-03-13
  • 修回日期:  2009-02-27
  • 刊出日期:  2009-04-15

目录

    /

    返回文章
    返回