Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem
Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem
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DOI：
10.1016/j.jfa.2016.01.002
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发表时间：
2014-10
影响因子：
1.7
通讯作者：
Matthias Schulte;C. Thaele
中科院分区：
文献类型：
--
作者：
Matthias Schulte;C. Thaele
本文给出了一个中等偏差原理以及中等偏差和大偏差不等式，它们适用于与等规高斯过程相关的固定Wiener混沌中的元素序列。所得结果的条件与著名的Nualart和Peccati四阶矩定理的条件一致。证明依赖于累积量的精确估计。作为应用，考虑了布朗单的爆炸积分、分数布朗运动的二次变分的离散化形式和球面高斯随机场的样本双谱。
A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown. The conditions under which the results are derived coincide with those of the celebrated fourth moment theorem of Nualart and Peccati. The proofs rely on sharp estimates for cumulants. As applications, explosive integrals of a Brownian sheet, a discretized version of the quadratic variation of a fractional Brownian motion and the sample bispectrum of a spherical Gaussian random field are considered.