MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

doi:10.1016/S0252-9602(10)60175-0

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1819-1836.doi: 10.1016/S0252-9602(10)60175-0

• 论文 • 上一篇

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

吴臻, 肖华

1.School of Mathematics, Shandong University, Jinan 250100, China
2.School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China

收稿日期:2006-10-22 修回日期:2008-11-29 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
Wu acknowledges the National Natural Science Foundation (10371067), the National Basic Research Program of China (973 Program, 2007CB814904), the Natural Science Foundation of Shandong Province (Z2006A01), the Doctoral Fund of Education Ministry of China, and Youth Growth Foundation of Shandong University at Weihai, P.R.China. Xiao acknowledges the Natural Science Foundation of Shandong Province (ZR2009AQ017), and Independent Innovation Foundation of Shandong University, IIFSDU.

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

WU Zhen, XIAO Hua

1.School of Mathematics, Shandong University, Jinan 250100, China
2.School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China

Received:2006-10-22 Revised:2008-11-29 Online:2010-09-20 Published:2010-09-20
Supported by:
Wu acknowledges the National Natural Science Foundation (10371067), the National Basic Research Program of China (973 Program, 2007CB814904), the Natural Science Foundation of Shandong Province (Z2006A01), the Doctoral Fund of Education Ministry of China, and Youth Growth Foundation of Shandong University at Weihai, P.R.China. Xiao acknowledges the Natural Science Foundation of Shandong Province (ZR2009AQ017), and Independent Innovation Foundation of Shandong University, IIFSDU.

摘要/Abstract

摘要：

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result
of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关键词: backward stochastic differential equations, comparison theorem, local time

Abstract:

Key words: backward stochastic differential equations, comparison theorem, local time

中图分类号:

60H10

吴臻, 肖华. MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM[J]. 数学物理学报(英文版), 2010, 30(5): 1819-1836.

WU Zhen, XIAO Hua. MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM[J]. Acta mathematica scientia,Series B, 2010, 30(5): 1819-1836.

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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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