论文标题
泊松空间上卡巴诺夫 - 基洛霍德积分的正常近似
Normal approximation of Kabanov-Skorohod integrals on Poisson spaces
论文作者
论文摘要
我们考虑了一般泊松空间上Kabanov-Skorohod积分的正常近似。我们的边界是Wasserstein和Kolmogorov距离，仅涉及Kabanov-Skorohod积分集成的差异操作员。这些证明依赖于Malliavin-Stein方法，尤其是按零件公式进行集成的多种应用。作为示例，我们研究了一些点过程的线性统计数据，这些过程可以通过泊松嵌入和功能与泊松过程的最佳点相关的功能来构建。
We consider the normal approximation of Kabanov-Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov-Skorohod integral. The proofs rely on the Malliavin-Stein method and, in particular, on multiple applications of integration by parts formulae. As examples, we study some linear statistics of point processes that can be constructed by Poisson embeddings and functionals related to Pareto optimal points of a Poisson process.
