空间布朗单由蔓延导致的占有测度分析  

Analysis on Occupation Measure of Spatial Brownian Sheet Which Come from Local Propagation on Line

作　　者：倪文清[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《福建师范大学学报（自然科学版）》2006年第1期7-11,共5页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(A10271027);福建省自然科学基金资助项目(F0210015)

摘　　要：设{Ws,t}是一取值于Rd(d≥3)的布朗单,qd表B esse l函数Jd2-2(x)的第一正零点,b是任意正实数.令p0,q0>0,k0=m in{p0,q0},Δb=[p0,p0+b]×[q0,q0+b],用μΔWb.,.(B(x,ε))表{Ws,t}在指标区间Δb内,在中心为x,半径为ε的球B(x,τ)里由直线上局部蔓延导致的占有测度.对任给a∈(0,4k0q2d),则使得lim supε→0μWΔ.,.b(B(Ws,t,ε))4ε(logε5)-1≥a的(s,t)∈Δb点的集合的H ausdorff维数a.s.大于等于2-k0aq2d4.Suppose that {Ws,t} is a two-parameter Brownian sheet in R^d（d ≥ 3） , that qd denotes the first posilive zero of the Bessel functions Jd/2-2（x） , and that b〉 0,P0,q0〉 0,k0 = min{p0,q0},△b=[p0,p0＋b]×[q0,q0＋b]. Let ^-μw△b…（B（x,ε）） denote the occupation measure of spatial Brownian sheet which come from the local propagation of thick points on line in the interval △b and in the ball B（Ws,t,ε）. For any a∈（0,4/k0qd^2）, it is proved that the Hausdorff dimension of the set consisting of all of （s,t） ∈△b such that lim（t→0）sup^-μw△b…（B（x,ε））/ε^1（｜log ε｜^5）^-1≥a is a.s.greater than or equal to 2-k0qd^2/4.

关 键 词：布朗单 占有测度 局部蔓延 HAUSDORFF维数 

分 类 号：O211.6[理学—概率论与数理统计]