论文标题
Dawson-Watanabe超级过程的功能性ITO形式
A Functional Ito-Formula for Dawson-Watanabe Superprocesses
论文作者
论文摘要
我们为Dawson-Watanabe Superprocess（一种众所周知的一类测量值过程）得出了ITO-Formula，该过程扩展了经典的ITO-Formula相对于两个方面的扩展。首先，我们将基础过程的状态空间扩展到[0，t]} $ in [0，t]} $的状态空间_ {t \ in [0，t]} $到无限维度的一个 - 有限度量的空间。其次，我们将公式扩展到函数$ f（t，x_t）$，具体取决于整个路径$ x_t =（x（x（s \ wedge t））_ {s \ in [0，t]} $ times $ t $。后来的扩展通常称为功能性ITO-formula。最后，我们评论了与超级过程相关的Martingales的可预测表示的应用。
We derive an Ito-formula for the Dawson-Watanabe superprocess, a well-known class of measure-valued processes, extending the classical Ito-formula with respect to two aspects. Firstly, we extend the state-space of the underlying process $(X(t))_{t\in [0,T]}$ to an infinite-dimensional one - the space of finite measure. Secondly, we extend the formula to functions $F(t,X_t)$ depending on the entire paths $X_t=(X(s\wedge t))_{s \in [0,T]}$ up to times $t$. This later extension is usually called functional Ito-formula. Finally we remark on the application to predictable representation for martingales associated with superprocesses.
