唐加山.一类超一致椭圆扩散过程的极限定理(英文)[J].数学研究及应用,2002,22(3):345~350 |
一类超一致椭圆扩散过程的极限定理(英文) |
Limit Theorems of a Class of Super-Uniformly Elliptic Diffusions |
投稿时间:1999-09-14 |
DOI:10.3770/j.issn:1000-341X.2002.03.005 |
中文关键词: |
英文关键词:uniformly elliptic diffusion superproces limit theorem. |
基金项目: |
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中文摘要: |
本文研究了分支特征为ψ(x,z)=γz1+β(0<β≤1)形式的超一致椭圆扩散过程,当初始值X0(dx)为底过程的某类不变测度时,给出了当空间维数d满足βd≤2时,超过程Xt依分布收敛于0测度,当βd>2时,Xt则依分布收敛于一个非退化的随机测度. |
英文摘要: |
In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < β≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense. |
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