Banach空间值的Ito积分及其性质

Ito Integral and Its Properties of Banach Space Value

设(Ω,F,{Ft}t≥0,P)为过滤概率空间,X,Y为Banach空间,{Mt}t≥0为Banach空间X值的连续(P,{Ft}t≥0)-鞅;f(.,.):[0,∞)×Ω→L(X,Y)为连续算子值的随机过程f(s,w)s≥0.给出It积分∫t0f(s,w)dMs的定义,并证得It型不等式,为讨论Banach空间Y值的随机微分方程奠定了基础.

Suppose（ Ω,F,{F t}t≥0,P} to be filtering probability space,X,Y is Banach space,{Mt}t≥0 is the continuous {P, {F t}t≥0}-martingale for the value of Banach space X, f（·,·）：[0,∞）×Ω→L（X,Y） is the random process of the value of the continuous operator f（s,w）s≥0.In this paper,the definition of It integral is given,which is ∫t0f（s,w）dMs,and the It-type inequality is proved,Banach space Y to discuss the value of the foundation of Stochastic Differential Equations.