CAJ | 학술논문

本文研究了从x出发的非线性漂移布朗运动的极大值、极小值和首达时问题.利用测度变换以及布朗运动的一些重要性质,如反射原理,增量的独立性等,获得了两种极值分布函数的精确表达式,得到了首达时的分布函数.结果表明,线性漂移布朗运动的极大值极小值以及首达时的分布问题的有关结果是本文结论的推论,最后给出一个例子.
본문연구료종x출발적비선성표이포랑운동적겁대치、겁소치화수체시문제.이용측도변환이급포랑운동적일사중요성질,여반사원리,증량적독립성등,획득료량충겁치분포함수적정학표체식,득도료수체시적분포함수.결과표명,선성표이포랑운동적겁대치겁소치이급수체시적분포문제적유관결과시본문결론적추론,최후급출일개례자.
In this article,we discuss the problem of extreme value for Brownian motion with nonlinear drift and study the distribution of the maximum value and minimum value and the first passage time. By using measure change and some important properties, such as, reflection property and the independence of increment, we obtain the exact expression for the distributions of two kinds of extreme values and also get the distribution of the first passage time. The conclusion shows that the result on extreme value for Browninn motion with linear drift is a corollary here.At last, we give an example and get the figure of the probability of the first passage time.