Brown运动与相关随机过程的极限定理

布朗运动与相关随机过程的极限定理是概率论极限理论的重要内之一。本项目研究布朗运动的收敛性质，以及分数布朗运动，稳定过程等一些随机过程的极限定理。研究的主要内容是：布朗运动增量的拟必然泛函极限定理，分数布朗运动的增量的泛函极限定理与局部泛函极限定理，分数布朗运动的增量在Holder范数下的泛函极限定理，稳定过程及相关随机过程的极限定理。. 另外，还研究偏差不等式与其他问题。

Limit theorems of Brownian motion and related stochastic processes are one of the important content for limit theory of probability theory. In this program, we investigate properties of convergence for Brownian motion, and limit theorems for a fractional Brownian motion and stable processes etc. Main content of investigation is : Quasi sure functional limit theorems for increments of Brownian motion , functional limit theorems and local functional theorems for increments of fractional Brownian motion, functional limit theorems for increments of fractional Brownian motion in the Holder norm,and limit theorems for stable processes and related stochastic processes.. In addition, deviation inequalities and other questions are also investigated.