由马氏链驱动的正倒向随机微分方程  

Forward-backward stochastic differential equations on Markov chains

作　　者：肖新玲[1] XIAO Xin-ling(School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, Shandong, China)

机构地区：[1]山东师范大学数学与统计学院,山东济南250014

出　　处：《山东大学学报（理学版）》2018年第4期46-54,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金青年科学基金资助项目(11301309);山东师范大学教改项目(2016JG28);山东师范大学数学与统计学院青年专项基金资助项目(shxzhxxm201503)

摘　　要：主要研究由马氏链驱动的完全耦合的正倒向随机微分方程(forward-backward stochastic differential equation,FBSDE)解的存在唯一性;采用在研究通常的完全耦合的FBSDE时常用的连续性方法,通过半鞅的Ito乘积法则与Lebesgue控制收敛定理,运用迭代法得到由马氏链驱动的完全耦合的FBSDE解的存在唯一性定理。In this paper,we mainly study the solutions about fully coupled forward-backward stochastic differential equations（FBSDE） on Markov chains. Using the usual method of continuation which is used to study fully coupled forward-backward stochastic differential equations,the Ito product rule of semimartingales,the Lebesgue control convergence theorem and iterative method,theorems about the solutions of the fully coupled forward-backward stochastic differential equations on Markov chains are obtained.

关 键 词：正倒向随机微分方程 解的存在唯一性 马氏链 

分 类 号：O211.63[理学—概率论与数理统计]