论文标题
复合鹰队功能的正常近似
Normal approximation of compound Hawkes functionals
论文作者
论文摘要
我们通过正态分布的随机变量在Wasserstein距离中得出定量界限，以相对于Hawkes过程的随机积分近似。在确定性和非阴性整合体的情况下，我们的估计仅涉及整数的第三刻，除了使用集成的平方规范的方差项。结果，我们能够观察到“第三刻现象”，其中第一个累积剂消失可以导致更快的收敛速率。我们的结果还应用于复合鹰派过程，并改善了当前文献，即估计可能不会在很长的时间内收敛到零，或者仅对特定核（例如指数或Erlang内核）获得。
We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. In the case of deterministic and non-negative integrands, our estimates involve only the third moment of integrand in addition to a variance term using a square norm of the integrand. As a consequence, we are able to observe a "third moment phenomenon" in which the vanishing of the first cumulant can lead to faster convergence rates. Our results are also applied to compound Hawkes processes, and improve on the current literature where estimates may not converge to zero in large time, or have been obtained only for specific kernels such as the exponential or Erlang kernels.
