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高维Wiener sausage的强逼近 被引量：1

Strong approximation of high dimensional Wiener sausage
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摘要 本文研究了四维及四维以上的Wiener sausage的体积,得到它们可以由一维Brown运动强逼近.作为应用,推出了弱收敛和重对数率. In this paper, we study the volume of Wiener sausage in R^d for d ≥ 4. We obtain that it can be strongly approximated by a one-dimensional standard Brownian motion. As an application, we give the weak convergence and laws of the iterated logarithm.
作者 王艳清
机构地区 中南财经政法大学统计与数学学院
出处 《中国科学：数学》 CSCD 北大核心 2011年第9期789-796,共8页 Scientia Sinica：Mathematica
基金 国家自然科学基金(批准号:10871153) 中央高校基本科研业务费专项资金(批准号:2011084 2010014)资助项目
关键词 WIENER SAUSAGE 强逼近 Skorohod 嵌入定理 Wiener sausage, strong approximation, Skorohod＇s representation theorem
分类号 O211.4 [理学—概率论与数理统计]
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参考文献17

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同被引文献15

  • 1It5 K, Jr McKean H P. Diffusion Processes and Their Sample Paths. New York: Springer, 1974.
  • 2Le Gall J F. Fluctuation results for the Wiener sausage. Ann Probab, 1988, 16:991-1018.
  • 3Cski E, Hu Y. Strong approximations of three-dimensional Wiener sausages. Acta Math Hungar, 2007, 114:205-226.
  • 4van den Berg M, Bolthausen E, Den Hollander F. Moderate deviations for the volume of the Wiener sausage. Ann Math, 2001, 153:355-406.
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  • 8van den Berg M, Bolthausen E, Den Hollander F. On the volume of the intersection of two Wiener sausages. Ann Math, 2004, 159:741-782.
  • 9KSnig W, MSrters P. Brownian intersection local times: Upper tail asymptotics and thick points. Ann Probab, 2002, 30:1605-1656.
  • 10Cao F Q, Wang Y Q. Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages. Electron J Probab, 2009, 14:1900-1935.

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中国科学：数学
2011年 第9期

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