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Lévy过程驱动的倒向重随机Volterra积分方程的对称解

Symmetric Solutions of Backward Doubly Stochastic Volterra Integral Equations Driven by Lévy Processes
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摘要 考虑一类由Lévy驱动的倒向重随机Volterra积分方程,首先在系数不依赖于变量(Y,Z)的情况下证明了方程对称解的存在唯一性.对一般情形,在全局Lipschitz假设条件下,利用不动点定理给出了方程对称解的存在唯一性定理. A class of backward doubly stochastic Volterra integral equations driven by Teugel＇s martingales and two mutually independent Brownian motions is considered. The existence and uniqueness of symmetric solutions for the equations with coefficient independent of variables （Y, Z） is investigated. For the general equations under global Lipschitz condition, we prove the existence and uniqueness of symmetric solutions using fixed point theorem.
作者 刘存霞 吕文
机构地区 烟台大学数学与信息科学学院
出处 《烟台大学学报（自然科学与工程版）》 CAS 2014年第2期79-83,共5页 Journal of Yantai University(Natural Science and Engineering Edition)
基金 山东省高校科研计划项目(J13LI06) 烟台大学青年基金(SX11Z2)
关键词 倒向重随机Volterra积分方程 Teugels鞅 LÉVY过程 对称解 backward doubly stochastic Volterra integral equation Teugels martingale L6vy process symmetricsolution
分类号 O211.63 [理学—概率论与数理统计]
  • 相关文献

参考文献15

  • 1Pardoux E, Peng Shige. Adapted solution of a backward stochastic differential equation[ J]. Systems Control Lett, 1990, 14 : 55-61.
  • 2E1 Karoui N, Peng Shige, Quenez M. Backward stochas- tic differential equations in finance[ J]. Math Finance, 1997, 7 : 1-71.
  • 3Peng Shige. Backward stochastic differential equations and its application in optimal control [ J ]. Appl Math Optim, 1993, 27 : 125-144.
  • 4Hamadene S, Lepeltier J. Zero-sum stochastic differential games and backward stochastic differential equations [ J ]. Sys- tems Control Lett, 1995, 24: 259-263.
  • 5Nualart D, Schoutens W. Chaotic and predictable repre- sentations for L6vy processes [ J ]. Stochastic Process Appl, 2000, 90: 109-122.
  • 6Nualart D, Sehoutens W. Backward stochastic differential equations and Feynman-Kac formula for L6vy processes, with applications in finance [ J ]. Bernoulli, 2001,7 : 761-776.
  • 7Bahlali K, Eddahbi M, Essaky E. BSDE associated with Levy processes and application to PDIE [ J ]. Journal of Applied Mathematics and Stochastic Analysis, 2003, 16: 1-17.
  • 8Lin Jianzhong. Adapted solution of backward stochastic nonlinear Volterra integral equations [ J ]. Stochastic Ana Appl, 2002, 20: 65-183.
  • 9Hu Ying, Peng Shige. Adapted solution of backward semilinear stochastic evolutin equation [ J ]. Stochastic Analysis and Applications, 1991, 9: 445-459.
  • 10Yong Jiongmin. Backward stochastic Volterra integral e- quations and some related problems [ J ]. Stochastic Proc Appl, 2006, 116: 779-795.

二级参考文献13

  • 1Pardoux E, Peng shige. Adapted solution of a backward stochastic differential equation[ J]. Systems Control Lett, 1990, 14 : 55-61.
  • 2El Karoui N, Peng shige, Quenez M. Backward stochas-tic differential equations in finance[ J ]. Math Finance, 1997, 7: 1-71.
  • 3Peng shige. Backward stochastic differential equations and its application in optimal control [ J ]. Appl Math Optim, 1993, 27: 125-144.
  • 4Hamad'ene S, Lepeltier J. Zero-sum stochastic differenti- al games and backward stochastic differential equations [ J ]. Systems Control Lett, 1995, 24: 259-263.
  • 5Pardoux E, Peng shige. Backward doubly stochastic dif- ferential equations and systems of quasilinear SPDEs[ J]. Probab Theory Related Fields, 1994, 88: 209-227.
  • 6Nualart D, Schoutens W. Chaotic and predictable repre- sentations for L "evy processes [ J ]. Stochastic Process Appl, 2000, 90: 109-122.
  • 7Nualart D, Schoutens W. Backward stochastic differential equations and Feynman-Kac formula for L 'evy processes, with applications in finance[J]. Bernoulli, 2001,7: 761-776.
  • 8Bahlali K, Eddahbi M, Essaky E. BSDE associated with L'evy processes and application to PDIE [ J ]. Journal of Applied Mathematics and Stochastic Analysis, 2003, 16: 1-17.
  • 9Hu ying, Peng shige. Adapted solution of backward semilinear stochastic evolutin equation [ J ]. Stochastic analysis and applications, 1991,9: 445--459.
  • 10Lin jianzhong. Adapted solution of backward stochastic nonlinear Volterra integral equations [ J ]. Stochastic Anal Appl, 2002. 20: 65-183.
烟台大学学报（自然科学与工程版）
2014年 第2期

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