论文标题
限制用于Hermite驱动过程的积分功能的定理
Limit theorems for integral functionals of Hermite-driven processes
论文作者
论文摘要
考虑$ x（t）= \ int _ { - \ infty}^t x（t-u）dz_u $，$ t \ geq 0 $的移动平均过程$ x $的$ x $，其中$ z $是（非高斯）订单$ q \ geq 2 $和$ x：本文将波动为$ t \ to \ infty $的波动的形式的积分函数$ t \ mapsto \ int_0^{tt} p（x（x（s））ds $，如果$ p $是任何给定的polynomial函数的情况。它扩展了一项在Tran（2018）中发起的研究，其中仅考虑了二次案例$ p（x）= x^2 $，并且考虑了有限维分布的意义。
Consider a moving average process $X$ of the form $X(t)=\int_{-\infty}^t x(t-u)dZ_u$, $t\geq 0$, where $Z$ is a (non Gaussian) Hermite process of order $q\geq 2$ and $x:\mathbb{R}_+\to\mathbb{R}$ is sufficiently integrable. This paper investigates the fluctuations, as $T\to\infty$, of integral functionals of the form $t\mapsto \int_0^{Tt }P(X(s))ds$, in the case where $P$ is any given polynomial function. It extends a study initiated in Tran (2018), where only the quadratic case $P(x)=x^2$ and the convergence in the sense of finite-dimensional distributions were considered.
