矩阵值Ornstein-Uhlenbeck 过程的大偏差上界

摘要

本文研究了矩阵值Ornstein-Uhlenbeck 过程的大偏差问题。通过构造指数鞅，得到了矩阵值Ornstein-Uhlenbeck过程的经验谱过程的大偏差上界，推广了厄米特布朗运动相应的结果。%In this paper, we study the large deviation problem for the matrixvalued Ornstein-Uhlenbeck processes. By constructing the exponedtial martingale, we obtain a large deviation upper bound for its empirical process, which extends the corresponding result for Hermitian Brownian motion.