具有绝对连续测度状态的超布朗运动  

SUPER-BROWNIAN MOTIONS WITH ABSOLUTELY CONTINUOUS MEASURE STATES

作　　者：任艳霞[1] 

机构地区：[1]北京大学数学科学学院概率统计系,北京100871

出　　处：《数学年刊（A辑）》2002年第4期493-504,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10001020)与国家优秀博士论文作者专项基金资助的项目.

摘　　要：设X={Xt,Pμ}是d维超布朗运动,具有分支率函数A与一般分支机制ψ.讨论A满足什么条件时可以保证Xt具有绝对连续状态.特别当ψ（s,x,z）=z2时,Dawson与Fleischmann[2]讨论了类似问题.本文对他们的讨论进行了改进,将他们的结果推广到了ψ一般的情形,并且简化了他们对A所加的条件.Suppose X = {Xt,Pμ} is a d-dimensional super-Brownian motion with branching rate function A and general branching mechanism ψ. It discusses conditions on A to guarantee that Xt has absolutely continuous states. For the particular case of ψ(s, x, z) = z2, the analogous problem has been discussed by Dawson and Fleischmann[2]. The author generalizes and simplifies the conditions of Dawson and Fleischmann based on an improvement on their argument.

关 键 词：绝对连续测度状态 超布朗运动 基本解 分支率函数 

分 类 号：O211.6[理学—概率论与数理统计]