布朗运动几种变化形式的概率性质及其应用

Probabilistic properties and applications of several variations of Brownian motion

在标准布朗运动的基础上,讨论了与标准布朗运动有关的几种变化形式的概率分布和联合分布。推导给出了其高阶原点矩的计算公式,给出了标准布朗运动在给定区间上最值的矩母函数的表达式。最后结合实例给出上述结论在证明概率不等式和估计概率界方面的应用。

On the basis of standard Brownian motion, this paper discusses several kinds of variations related to standard Brownian motion in the form of probability distribution and joint distribution. The formula for calculating the higher order moment of origin is derived, and the formula for moment generating function of the maximum value of the standard Brownian motion on a given interval is given. Finally, the applications of the above conclusions in proving probability inequalities and estimating probability bounds are given by examples.