摘要
引言 [1]中的正交随机测度论概括了多种不能按轨道进行的随机积分,当然最典型的代表是可料过程对平方可积鞅的随机积分。但是在试图把被积函数从可料扩充到可选时,就只有限制在拟左连续(局部)平方可积鞅的情形才得到满意的结果。鞅具有可料跳对积分的正交性似乎是一种障碍。在半鞅的积分表示中有一项表示跃度有界的纯断鞅部分,它表成了对跃度点过程补偿的积分,既然积出来是局部平方可积鞅,自然可以设想。
Stochastic integrals with respect to the compensations of point processes are pure-disconti-nuous martingales.This fact suggests that there exists some relationship between S.M.(O) and such kind of stochastic integrals.In this paper,we discuss what kind of point processes can generate some S.M.(O)so that the above stochastic integrals can be regarded as S.I.with respect to the corresponding S.M.(O). We found the sufficient and necessary condition.called it 'Class (L) property'.Applying it to the jump point process of a pure-discontinuous martingale.'Class (L) property' is equivalent to the quasi-left continuity of the martingale.
出处
《应用数学学报》
CSCD
北大核心
1992年第1期1-9,共9页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金
