d>4情形下广义布朗单的截口常返性  

Section Recurrence of Generalized Brownian Sheet in the Case d>4

作　　者：朱能辉 周振强 ZHU Nenghui;ZHOU Zhenqiang(School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China)

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024

出　　处：《厦门理工学院学报》2021年第1期85-90,共6页Journal of Xiamen University of Technology

基　　金：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)。

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。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.

关 键 词：广义布朗单 区域常返 截口常返性 方差测度函数 

分 类 号：O211.6[理学—概率论与数理统计]