从x出发的漂移Brownian Motion的极值分布

THE DISTRIBUTIONS OF EXTREME VALUE FOR BROWNIAN MOTION WITH POSITIVE DRIFT STARTING FROM x

该文研究了从x出发的正漂移Brownian Motion的极值问题,给出了关于这种随机过程的两种极大值的定义,并主要利用Brownian Motion的一些重要性质,比如正交不变性、时空齐次性及在有限停时上的强Markov性等,获得了两种极大值的分布函数的精确表达式.

In this paper, we discuss the problem of extreme value for Brownian Motion with positive drift starting from. We define two kinds of maximum value for this stochastic process. Mainly by some important properties of Brownian Motion, such as, symmetry property, time-homogeneity and strong Markov property on a finite stopping time and so on, we obtain the exact expression for the distributions of two kinds of maximum value.