有限或无限区间连续生成元的一维反射倒向随机微分方程的惩罚方法  

Penalization Approach to One-Dimensional Reflected Backward Stochastic Differential Equations with Finite or Infinite Time Horizons and Continuous Generators

作　　者：石学军[1] 穆静静[1] 杨丛[1] 

机构地区：[1]中国矿业大学理学院,中国徐州221116

出　　处：《湖南师范大学自然科学学报》2013年第3期8-14,共7页Journal of Natural Science of Hunan Normal University

基　　金：中央高校基本科研业务费专用基金资助项目(2013DXS03);2013年江苏省普通高校研究生科研创新计划资助项目(CXZZ13-0921)

摘　　要：采用惩罚方法研究带单边连续障碍的无穷区间反射倒向随机微分方程(RBSDE).在生成元g满足广义线性增长且关于(y,z)连续的条件下,得到了RBSDE解的存在性;并且在g关于y满足广义Osgood条件且关于z满足广义一致连续条件下得到了解的比较定理,从而证明了此条件下RBSDE解的唯一性.By the penalization approach,the existence and comparison theorems of solutions to the reflected backward stochastic differential equations with lower continuous barrier（RBSDEs） are obtained,where the time horizon may be finite or infinite,the hypotheses on their generators g are not necessary to be uniform in t.There exists at least one solution to the RBSDEs whose generators are continuous and of linear-growth in（y,z）.Furthermore,if g satisfies Osgood condition in y and uniform continuity in z,comparison theorems will hold true.Then the uniqueness about their solutions follows easily from the comparison result.

关 键 词：反射倒向随机微分方程 无穷区间 存在唯一性定理 广义一致连续条件 Osgood条件 比较定理 

分 类 号：O211.63[理学—概率论与数理统计]