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

英文关键词:uniformly elliptic diffusion  superproces  limit theorem.

中文摘要:

      本文研究了分支特征为ψ（x,z）=γz^1+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X_t依分布收敛于0测度,当βd>2时,X_t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 {X_t,t ≥ 0} with its branching mechanism given by ψ(z) = γz^1+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 X_t will converge to the null in distribution and if βd > 2, then X_t will converge to a nondegenerative random measure in the same sense.