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Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (3): 355-366    DOI:
    
Functional sample path properties for subsequence's $\boldsymbol{C}$-$\boldsymbol{R}$ increments of $k$-dimensional Brownian motion in Holder norm
WEI Qi-cai
School of Math. & Com. Sci., Wuhan Polytechnic Univ., Wuhan 430023, China
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Abstract  In this paper, with aid of large deviation formulas established in strong topology generated by Holder norm for $k$-dimensional Brownian motion, the paper obtained the functional sample path properties for subsequence's $C$-$R$} increments of $k$-dimensional Brownian motion in Holder norm, by which one can get the functional laws of iterated logarithm for $k$-dimensional Brownian motion.

Key words$k$-dimensional Brownian motion      functional sample path properties      subsequence's $C$-$R$ increments      Holder norm     
Received: 07 August 2014      Published: 27 May 2018
CLC:  O211.6  
Cite this article:

WEI Qi-cai. Functional sample path properties for subsequence's $\boldsymbol{C}$-$\boldsymbol{R}$ increments of $k$-dimensional Brownian motion in Holder norm. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 355-366.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I3/355


$k$-维Brown运动子列$C$-$R$型增量在Holder范数下的泛函样本轨道性质

借助于$k$-维Brown运动在Holder范数生成的强拓扑下的大偏差公式, 得到了$k$-维Brown运动子列$C$-$R$型增量在Holder范数下的泛函样本轨道性质. 藉此性质, 可以得到$k$-维Brown运动在Holder范数下的泛函重对数定律.

关键词: $k$-维Brown运动,  泛函样本轨道性质,  子列$C$-$R$型增量,  Holder范数 
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