论文标题
关于计数过程的混乱扩展
On the chaotic expansion for counting processes
论文作者
论文摘要
我们介绍并研究了使用泊松嵌入代表的混沌扩展的替代形式。我们将此替代表格\ textit {pseudo-chaotic扩展}命名。作为一种应用，我们证明，对于任何线性鹰队过程，该伪骨化膨胀的系数都是以封闭形式获得的，而通常的混乱膨胀的系数不能明确得出。最后，我们通过以伪骨化形式构造一个过程的示例来进一步研究线性鹰队过程的结构，该过程满足了确定霍克斯过程的随机自我激发强度方程（尤其是其期望等于霍克斯的过程之一），但这是计数过程。
We introduce and study an alternative form of the chaotic expansion for counting processes using the Poisson imbedding representation; we name this alternative form \textit{pseudo-chaotic expansion}. As an application, we prove that the coefficients of this pseudo-chaotic expansion for any linear Hawkes process are obtained in closed form, whereas those of the usual chaotic expansion cannot be derived explicitly. Finally, we study further the structure of linear Hawkes processes by constructing an example of a process in a pseudo-chaotic form that satisfies the stochastic self-exciting intensity equation which determines a Hawkes process (in particular its expectation equals the one of a Hawkes process) but which fails to be a counting process.
