多重Wiener-Ito积分亦称Wiener-Ito混沌，是一种非常典型的非线性高斯泛函；由于具有丰富而深刻的性质，它成为了很常用的工具和活跃的研究对象。特别是近十多来年出现的多重Wiener-Ito积分的两个深刻性质：中偏差原理，及弱收敛的四阶矩定理及Stein方法得到的定量版本。申请人及其合作者建立了复多重Wiener-Ito积分和实多重Wiener-Ito积分之间的本质联系，并给出了四阶矩定理的两种证明。在此基础上，我们研究增量非平稳的自相似连续高斯过程驱动的一维和二维OU过程漂移系数最小二乘估计的强相合和渐进正态性，Berry-Esseen界。并且研究复多重Wiener-Ito积分的概率密度差的最大模意义下的四阶矩定理及其定量版本，和复多重Wiener-Ito积分的中偏差原理。前者涉及含有⼤参数的奇异的多重实积分的渐进展开，后者涉及复多重Wiener-Ito积分垒量的表出。

Multiple Wiener-Itô Integrals, or say Wiener-Ito chaos, are a typical type of nonlinear Gaussian functionals. They have been a very useful tools for probability and statistics and an active object to research since they have ample and deep properties. Especially, two properties such as moderate derivation principle and Fourth Moments Theorem and its quantitive version appeared during the last more than ten years. The author's recent joint works on complex Gaussian isonormal processes give two different proofs of complex fourth moment theorems, which establishes a crucial relationship between complex Wiener-Ito integrals and real Wiener-Ito integrals. Based on these work, we will explore the strong consistency, asymptotic normality, and Berry-Esseen bounds for the least squares estimation of the drift coefficient of both 1-dimensional and 2-dimensional OU processes with self-similar, continuous Gaussian processes that do not necessarily have stationary increments fractional noise. We will also explore the convergence in density of the normal approximation for the complex Wiener-Ito integrals and its quantitive version, and its moderate derivation principle. The former involves asymptotic approximations of multiple real integrals with big parameters, and the latter involves the representation of cumulants for complex Wiener-Ito integrals.