| 一类超一致椭圆扩散过程的极限定理 |
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| 引用本文： | 唐加山.一类超一致椭圆扩散过程的极限定理[J].数学研究及应用,2002,22(3):345-350. |
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| 作者姓名： | 唐加山 |
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| 作者单位： | 南京邮电学院应用数理系,江苏,南京,210003 |
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| 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.
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| 关 键 词： | 超一致椭圆扩散过程 极限定理 随机测度 |
| 收稿时间： | 1999/9/14 0:00:00 |
Limit Theorems of a Class of Super-Uniformly Elliptic Diffusions |
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| TANG Jia-shan.Limit Theorems of a Class of Super-Uniformly Elliptic Diffusions[J].Journal of Mathematical Research with Applications,2002,22(3):345-350. |
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| Authors: | TANG Jia-shan |
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| Affiliation: | Dept. of Appl. Math. & Phy.; Nanjing Univ. of Posts & Telecommunications; Jiangsu; China |
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| Abstract: | 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 initialvalue X0(dx) is one kind of invariant measures of the underlying processes, we show thatif dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null indistribution and if βd ＞ 2, then Xt will converge to a nondegenerative random measurein the same sense. |
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| Keywords: | uniformly elliptic diffusion superproces limit theorem |
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