一类连续半鞅型随机微分方程解的随机稳定性  

Stochastic Stabuity of Solution of a Class Contintions Semimartingale Type Stochas-tic Differential Equations

作　　者：张健 秦明达[1] 

机构地区：[1]北京科学技术大学数学力学系

出　　处：《数学学报（中文版）》1995年第6期776-781,共6页Acta Mathematica Sinica：Chinese Series

摘　　要：本文利用Ｌｙａｐｕｎｏｖ函数方法，讨论了时齐Ｄｏｌｅａｎｓ－Ｄａｄｅｒ－Ｐｒｏｔｔｅｒ方程ｄＸ＿ｔ＝σ（Ｘ＿ｔ）ｄＭ＿ｔ＝ｂ（Ｘ＿ｔ）ｄＡ＿ｔ＋（（Ｍ＿ｔ）为连续局部平方可积鞅；（Ａ＿ｔ）为连续有限变差过程）平凡解的随机稳定性。本文建立了随机稳定性的判定定理并给出了相应的Ｌｙａｐｕｎｏｖ函数的一种具体形式。Using the method of Lyapunov function, we will discuss the stochastic stability ofthe trivial solutions of Doleans-Dade-Protter equations dX_t=σ(X_t)dM_t+b(X_t)dA_t,where(M_t)is a continuous locally square integrable martingale and (A_t) is a continuous process with finitevariation. Also we will give the criterion of stocliastic stability and a specific Lyapunov function.

关 键 词：随机微分方程 连续半鞅 随机稳定性 

分 类 号：O211.63[理学—概率论与数理统计]