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数学进展 - 2018, Vol. 47(2): 277-286
研究论文
抽象Wiener空间上Brown运动增量关于${ {(r,p)}}$-容度的钟泛函重对数律
Chung's Functional Law of the Iterated Logarithm for Increments of a Brownian Motion with Respect to ${ {(r,p)}}$-capacities on an Abstract Wiener Space

刘永宏,李东升,李丰兵,姜淼
LIU Yonghong*, LI Dongsheng,LI Fengbing, JIANG Miao

广西高校数据分析与计算重点实验室;
桂林电子科技大学数学与计算科学学院,桂林, 广西, 541004
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation; School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, P. R. China

收稿日期: 2016-09-08
出版日期: 2018-05-16
2018, Vol. 47(2): 277-286
DOI: 10.11845/sxjz.2016108b


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摘要 应用Brown运动在Hölder范数下关于$(r,p)$-容度的大偏差和小偏差, 得到了Brown运动增量在Hölder范数下关于$(r,p)$-容度的钟泛函重对数律.
关键词 钟泛函重对数律$(r,p)$-容度lder范数Brown运动增量    
Abstract:Using large deviation and small deviation of a Brownian motion in Hölder norm with respect to $(r,p)$-capacities, Chung's functional law of the iterated logarithm for increments of a Brownian motion in Hölder norm with respect to $(r,p)$-capacity is derived.
Key wordsChung's functional law of the iterated logarithm    $(r,p)$-capacities       lder norm    increments of a Brownian motion
PACS:  O211.4  
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[6] Li, X.R. and Liu, Y.H., The rate of quasi sure convergence for increments of a Brownian motion in Hölder norm, Chin. Ann. Math. Ser. A, 2015, 36(2): 129-136 (in Chinese).
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[1] 刘永宏, 王为娜. Brown运动增量在Hölder范数下的局部Strassen重对数律[J]. 数学进展, 2019, 48(1): 121-127.
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