多参数广义布朗单的象与容度  

Multiparameter Generalized Brownian Sheet Images and Capacity

作　　者：陈振龙[1] 

机构地区：[1]浙江工商大学统计与数学学院,杭州310018

出　　处：《数学学报（中文版）》2009年第2期269-280,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(70871104)

摘　　要：研究了既没有平稳增量性,也没有scaling性质的N指标d维广义布朗单象的容度问题.证明了多参数广义布朗单具有扇局部不确定性,给出了一族多参数广义布朗桥的性质.应用这些结论,得到了多参数广义布朗单象集的Lebesgue测度与容度之间的关系,给出了其象集的确切容度估计.所得结果包含了布朗运动和布朗单的相应结果,也解决了Kahane提出的关于可加布朗运动的Bessel-Riesz容度问题.The problem of the capacity of the imange for N-parameter d-dimensional generalized Brownian sheet, which may satisfy neither scaling property nor stationary increments, is investigated. It is proved that the multiparameter generalized Brownian sheet have the sectorial local nondeterminism, and a family of generalized bridged sheets are also analyzed. The relationship between its image and the capacity is obtained by means of the sectorial local nondeterminism, and an explicit capacity estimate for its image is provided. The conclusions about the Brownian motion and the Brownian sheet can be considered as special cases of our results. A problem about the Bessel-Riesz capacity of the additive Brownian motion proposed by Kahane is also solved.

关 键 词：多参数 广义布朗单 象集 

分 类 号：O211.6[理学—概率论与数理统计]