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Lvy过程驱动的倒向重随机Volterra积分方程 被引量：1

Backward Doubly Stochastic Volterra Integral Equations Driven by a Lvy Process
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摘要 考虑一类由Teugels鞅和2个相互独立的布朗运动共同驱动的倒向重随机Volterra积分方程,在系数满足Lipschitz假设条件下,利用不动点定理证明了适应解的存在唯一性. A class of backward doubly stochastic Voherra integral equations driven by Teugel＇ s martingales and two mutually independent Brownian motions are investigated. Via fixed point theorem we prove the existence and uniqueness of adapted solution for those equations whose coeffients satisfy Lipschitz condition.
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 2012年第3期157-161,共5页 Journal of Yantai University(Natural Science and Engineering Edition)
基金 烟台大学青年基金(SX11Z2)
关键词 倒向重随机Volterra积分方程 Teugels鞅 Lvy过程 backward doubly stochastic Volterra integral equation Teugels martingale L^vy process
分类号 O211.63 [理学—概率论与数理统计]
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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.

同被引文献14

  • 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.

引证文献1

烟台大学学报（自然科学与工程版）
2012年 第3期

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