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具有一致连续生成元和可积参数的倒向随机微分方程 被引量：3

BSDEs with uniformly continuous generators and integrable parameters
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摘要 本文建立了具有可积参数的一维倒向随机微分方程(BSDE)的一个新的存在唯一性结果,其中BSDE的生成元g关于y满足Osgood条件且关于z是α-Hlder(0<α<1)连续的. This paper establishes a new existence and uniqueness result for solutions to one-dimensional backward stochastic differential equations （BSDEs） with only integrable parameters, where the generators of the BSDEs satisfy the Osgood condition in y, and they are α-Hlder （0 α 1） continuous in z.
作者 范胜君 江龙
机构地区 中国矿业大学理学院数学系
出处 《中国科学：数学》 CSCD 北大核心 2012年第2期119-131,共13页 Scientia Sinica：Mathematica
基金 国家自然科学基金(批准号:10971220 11101422) 教育部全国优秀博士学位论文作者专项基金(批准号:200919) 江苏省青蓝工程中青年学术带头人培养对象基金 中央高校基本科研业务费专项基金(批准号:2010LKSX04 JK111729)资助项目
关键词 倒向随机微分方程 可积参数 Osgood条件 Hlder连续 存在唯一性 backward stochastic differential equation integrable parameters Osgood condition Hlder continuous existence and uniqueness
分类号 O211.63 [理学—概率论与数理统计]
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参考文献15

  • 1Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation. Systems Control Lett, 1990, 14: 55-61.
  • 2Briand Ph, Delyon B, Hu Y, et al. L^p solutions of backward stochastic differential equations. Stochastic Process Appl, 2003, 108:109-129.
  • 3Briand Ph, Hu Y. BSDE with quadratic growth and unbounded terminal value. Probab Theory Related Fields, 2006, 136:604-618.
  • 4Briand Ph, Lepeltier J, San Martin J. One-dimensional BSDEs whose coefficient is monotonic in y and non-Lipschitz in z. Bernoulli, 2007, 13:80-91.
  • 5Fan S, Jiang L. Existence and uniqueness result for a backward stochastic differential equation whose generator is Lioschitz continuous in y and uniformly continuous in z. J Appl Math Comput, 2010, 36:1-10.
  • 6Fan S, Jiang L. Finite and infinite time interval BSDEs with non-Lipschitz coefficients. Statist Probab Lett, 2010, 80: 962-968.
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同被引文献37

  • 1Pavdoux E, Peng S G. Adapted Solution of a Backward Stochastic Differential Equation. Systems Control Lett., 1990, 14:55-61.
  • 2E1 Karoui N, Peng S G, Quenez M C. Backward Stochastic Differential Equations in Finance. Math- ematical Finance, 1997, 7(1): 1-71.
  • 3Briand Ph, Delyon B, Hu Y, Pardoux E, Stoica L. Lp Solutions of Backward Stochastic Differential Equations. Stochastic Process Appl., 2003, 108:109-129.
  • 4Lepeltier J P, San Martin J. Backward Stochastic Differential Equations with Continuous Coefficients. Statist. Probab. Lett., 1997, 34:425-430.
  • 5Hamadne S. Multidimensional Backward Stochastic Differential Equations with Uniformly Continu- ous Coefficients. Bernoulli, 2003, 9(3): 517-534.
  • 6Jia G Y. A Uniqueness Theorem for the Solution of Backward Stochastic Differential Equations. C. R. Acad. Sci. Paris, Ser I, 2008, 346:439-444.
  • 7Mao X R. Adapted Solutions of Backward Stochastic Differential Equations with Non-Lipschitz Cof- ficients. Stochastic Process Appl., 1995, 58:281-292.
  • 8Pardoux E. BSDEs, Weak Convergence and Homogenization of Semilinear PDEs. Nonlinear Analysis, Differential Equations and Control. Kluwer Acad Pub, 1999, 503-549.
  • 9Fan S J, Liu D Q. A Class of BSDEs with Integrable Parameters. Statist Probab. Lett., 2010, 80(23-24): 2024-2031.
  • 10Xiao L X, Li H Y, Fan S J. One Dimensional BSDEs with Monotonic, H61der Continous and Integrable Parameters. J. East China Normal University Natural Sciences, 2012, 1:130-137.

引证文献3

二级引证文献2

中国科学：数学
2012年 第2期

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