Banach空间值的Ito积分及其性质  

Ito Integral and Its Properties of Banach Space Value

作　　者：张瑶[1] 王玉文[1] 

机构地区：[1]哈尔滨师范大学

出　　处：《哈尔滨师范大学自然科学学报》2011年第2期27-31,共5页Natural Science Journal of Harbin Normal University

基　　金：国家自然科学基金项目资助(11071051)

摘　　要：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.

关 键 词：BANACH空间 连续鞅 Ito积分 Ito型不等式 

分 类 号：O177.2[理学—数学]