论文标题
强尾累积过程的强高斯近似
Strong Gaussian approximation for cumulative processes with heavy tails
论文作者
论文摘要
本文是工作的延续：2006.09583致力于建立累积过程的强大不变性原理中的收敛速率。我们在再生周期和增量上的增量仅具有大于2的功率矩时，建立了最佳的收敛速度。在这种功率类型条件下，证明了两种类型的维也纳过程近似近似值：strassen的不变性原则和不平等的收敛速率，使得随机偏离近似值的可能性偏差。
This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration periods and increments over them have only power moments of order greater than 2. Under this power-type conditions two types of approximation by Wiener process are proved: the rate of convergence in the Strassen's invariance principle and inequalities for the probability that random process deviates from the approximating one.
