Existence, Uniqueness and Approximation for Lp Solutions of Reflected BSDEs with Generators of One-sided Osgood Type  

作　　者：Sheng Jun FAN 

机构地区：[1]School of Mathematics, China University of Mining and Technology, Xuzhou 221116, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2017年第6期807-838,共32页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11371362);the Fundamental Research Funds for the Central Universities(Grant No.2012QNA36)

摘　　要：We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.

关 键 词：Reflected backward stochastic differential equation Lp solutions comparison theorem one-sided Osgood condition uniform continuity condition 

分 类 号：O211.63[理学—概率论与数理统计] O175.1[理学—数学]