Some Polar Sets for the Generalized Brownian Sheet  

作　　者：LI Huiqiong LIU Luqin CHEN Zhenlong 

机构地区：[1]College of Statistics and Mathematics, Zhejiang GongshangUniversity, Hangzhou 310018, Zhejiang, China [2]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2008年第2期137-140,共4页武汉大学学报（自然科学英文版）

基　　金：the National Natural Science Foundation of China (10471148);the Natural Science Foundation of Shaanxi Province (2005A08, 2006A14)

摘　　要：Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.

关 键 词：generalized Brownian sheet polar set single point multiple points 

分 类 号：O211.6[理学—概率论与数理统计]