Vol.20 No.4 张艳等：倒向随机微分方程的随机稳定性 ·393· av. av. 由()知+L'v00,》d≥0.所以有，Ea+L~v00,01F小20(=1.2…m网 由(0.0)式知，Ey0))lF]≤0))a.s.(=1,2,…,m),即{V00,0,F}(G= 1,2,…,m)是反正上鞅； (i)由于V(y,)连续且V(0,)=0,故e>0,e>0,TD0,总存在一正数δ=6(T,e,e)<e, 使当1g1≤ò时就有(0.1)式：三化，)<ae)·e.另外，由⑩知{00，，F}i=1,2.…,m是 反正上鞅，从而(200，)，F}也是反正上鞅，于是当1G1≤0时，由反正上鞅不等式（引理1） 及(0.1)式：有： 含g刀 <Ei E[O,T] a(e) 再由条件(H,)易得Pr 灯0之“，同随机系统(o的平只解是道机稳定的。 ∈0，T] 参考文献 1 Peng S.A General Stochastic Maximum Principle for Optimal Control Problems.SIAM J Contorl Opim,1990,28(4):966 2 Gihman II.Differential Equation with Random Function.Kiev:Akad Nauk Ukrain SSR,1964.41 3胡宜达.随机微分方程稳定性理论.南京：南京大学出版社，1990.93 4 Peng S.Adapted Solution of Backward Stochastic Equation.System Control Lett,1990,14:55 Stochastic Stability of Backward Stochastic Differential Equation of Ito Type Zhang Yan Oi Mingda Applied Science School,UST Beijing,Beijing 100083,China ABSTRACT Some concepts such as inverse brownian motion,inverse martingle are introduced,and relative properties are investigated.By the method of Lyapunov function, the stochastic stability of backward stochatic differenttial equation(BSDE)of Ito type is dy,=b(y 1)dr+av t)dw E[O,T] studied as follow y(T)=a.s KEY WORDS backward stochastic differential equation;inverse Brown motion;inverse martingle;stochastic stability