由马氏链驱动的正倒向随机微分方程比较定理  

Comparison Theorems for Forward-Backward Stochastic Differential Equations on Markov Chains

作　　者：肖新玲[1] 王秀丽[1] 

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：《济南大学学报（自然科学版）》2017年第5期466-469,共4页Journal of University of Jinan(Science and Technology)

基　　金：国家自然科学基金青年科学基金项目(11301309);山东师范大学教学改革研究项目(2016JG28);山东师范大学数学与统计学院青年专项基金项目(shuxzhxxm201503)

摘　　要：为了研究由马氏链驱动的完全耦合的正倒向随机微分方程的比较定理,采用在研究通常的完全耦合的正倒向随机微分方程时常用的连续性方法,通过运用半鞅的Ito乘积法则与Lebesgue控制收敛定理,得到由马氏链驱动的完全耦合的正倒向随机微分方程的2个关于初值的比较定理。结果表明,对于2个结构相同、仅过程X_t的初值X_0不同的由马氏链驱动的完全耦合的正倒向随机微分方程,在正向过程X_t与倒向过程Y_t这2个过程的取值都是一维实数值,并且在2个正倒向随机微分方程都满足单调性条件,从而解都存在且唯一的条件下,X_0越大,则过程Y_t的初值Y_0越大。To study the comparison theorems of fully coupled forward-backward stochastic differential equations on Markov chains, using the method of continuation usually used to study fully coupled forward-backward stochastic differential equations, the Ito product rule of Semimartingales, and the Lebesgue control convergence theorem, two comparison theo- rems of the fully coupled forward-backward stochastic differential equations on Markov chains for solutions of initial values were obtained. The results show that for the two forward-backward stochastic differential equations on Markov chains with the same structure and different initial values, if all of the values of Xt and Y~ are real numbers, and the two forward- backward stochastic differential equations satisfy the monotonicity conditions so that each forward-backward stochastic differential equation has a unique solution, then the greater X0 is, the greater the initial value Y0 of the process Y~ is.

关 键 词：正倒向随机微分方程 比较定理 马氏链 

分 类 号：O211.63[理学—概率论与数理统计]