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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.
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Basic Information:
DOI:10.12194/j.ntu.20200101001
China Classification Code:O211.1;O552.1
Citation Information:
[1]JIANG Peihua,ZHOU Qiaoyan,LAN Tianya ,et al.Probabilistic properties and applications of several variations of Brownian motion[J].Journal of Nantong University (Natural Science Edition),2022,21(01):88-94.DOI:10.12194/j.ntu.20200101001.
Fund Information:
安徽省高校自然科学基金重点项目(KJ2019A0161); 国家基金预研项目(Xjky08201903); 国家社会科学基金一般项目(18BTJ034); 安徽工程大学人才培育科研启动基金(S022022014); 教育部产学研合作协同育人项目(202102218020)
2022-03-20
2022-03-20