论文标题
限制在多个随机积分上保守流动的定理
Limit Theorems for Conservative Flows on Multiple Stochastic Integrals
论文作者
论文摘要
我们考虑由多个随机积分和无限测量的保守动力系统构建的固定序列$（x_n）$。定义多个积分的随机度量是非高斯的，无限分开，并且具有有限的差异。关于动态系统的一些其他假设产生了（0,1）$量化系统保守性的参数$β\。该参数$β$以及整体的顺序决定了$（x_n）$的协方差的衰减率。本文的目的是建立$（x_n）$的部分总和过程的限制定理。当协方差衰减足够快时，我们以布朗运动为限制获得了一个中央限制定理，而在协方差衰减足够缓慢时，具有分数的布朗尼运动或rosenblatt过程的非中心极限定理作为限制。
We consider a stationary sequence $(X_n)$ constructed by a multiple stochastic integral and an infinite-measure conservative dynamical system. The random measure defining the multiple integral is non-Gaussian, infinitely divisible and has a finite variance. Some additional assumptions on the dynamical system give rise to a parameter $β\in(0,1)$ quantifying the conservativity of the system. This parameter $β$ together with the order of the integral determines the decay rate of the covariance of $(X_n)$. The goal of the paper is to establish limit theorems for the partial sum process of $(X_n)$. We obtain a central limit theorem with Brownian motion as limit when the covariance decays fast enough, as well as a non-central limit theorem with fractional Brownian motion or Rosenblatt process as limit when the covariance decays slow enough.
