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[1]朱能辉,周振强.d>4情形下广义布朗单的截口常返性[J].厦门理工学院学报,2021,29(1):85-90.[doi:1019697/jcnki16734432202101013]
 ZHU Nenghui,ZHOU Zhenqiang.Section Recurrence of Generalized Brownian Sheet in the Case d>4[J].Journal of JOURNAL OF XIAMEN,2021,29(1):85-90.[doi:1019697/jcnki16734432202101013]
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《厦门理工学院学报》[ISSN:1673-4432/CN:35-1289/Z]

卷:
29
期数:
2021年第1期
页码:
85-90
栏目:
应用数理科学
出版日期:
2021-02-28

文章信息/Info

Title:
Section Recurrence of Generalized Brownian Sheet in the Case d>4
文章编号:
16734432(2021)01008506
作者:
朱能辉周振强
厦门理工学院应用数学学院,福建 厦门 361024
Author(s):
ZHU NenghuiZHOU Zhenqiang
School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China
关键词:
广义布朗单区域常返截口常返性方差测度函数
Keywords:
generalized Brownian sheetregional recurrencesections recurrencevariance measure function
分类号:
O2116
DOI:
1019697/jcnki16734432202101013
文献标志码:
A
摘要:
为研究广义布朗单在d>4且满足一般条件下的截口常返性,基于方差测度函数等高线上的点所对应的t轴纵坐标,利用数学归纳法定义指标集的s轴区间的可数个分划点,再利用纵坐标和分划点,将指标集可数分割为位于有限个等高线间的矩形块,从而把广义布朗单的截口常返性集转化为指标集为上述矩形块的截口常返性集的并集。在假设方差测度函数的等高线与指标集的s轴所围成部分的方差测度有上界的条件下,结合BorelCantelli引理,证明P{s >0,使得过程t→W(s,t)是区域常返}=0。研究结果表明:当d>4时,广义布朗单是非截口常返的,且所需要的条件对于常见的LebegueStieltjes测度均满足。
Abstract:
To study the sections recurrence of generalized Brownian sheets under d>4 and in general conditions,countable points of the saxis interval of the index set are defined by mathematical induction based on the vertical coordinate of the taxis corresponding to the points on the contour line of the variance measure function,the index set numerically divided into rectangular blocks located between finite contour lines using the vertical coordinates and dividing points,and the index set of the generalized Brownian sheet transformed into the union of the index set of the truncated recurrence set of the rectangular blocks.Under the assumption that the variance measure enclosed by the saxis of the index set and the contour line of the variance measure function have an upper bound,it is then proved that P{s>0,such that t→W(s,t) is regional recurrent}=0 by combining BorelCantelli Lemma.The results show that when d>4,the generalized Brownian sheet is not section recurrent and the required conditions are satisfied for the common LebegueStieltjes measure.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:20201125修回日期:20210107 基金项目:福建省教育厅中青年教师教育科研项目(JT180444);福建省自然科学基金青年项目(2020J05234);厦门理工学院科研攀登计划项目(XPDKT20037) 通信作者:朱能辉,男,讲师,博士,研究方向为概率论、非参数半参数统计,Email:2015000049@xmut.edu.cn。
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