ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES  

作　　者：陈振龙 

机构地区：[1]College of Statistics and Mathematics, Zhejiang Gongshang University

出　　处：《Acta Mathematica Scientia》2014年第1期141-161,共21页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11371321);Zhejiang Provincial Natural Science Foundation of China(Y6100663);the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statis-tics of Zhejiang Gongshang University)

摘　　要：Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.

关 键 词：INTERSECTION diffusion processes hitting probability polar set HAUSDORFFDIMENSION 

分 类 号：O211.6[理学—概率论与数理统计] TP391.41[理学—数学]