超布朗运动:质量过程的极限行为及值空间的扩张

Super-Brownian Motion: The Limiting Behaviour of the Mass Process and the Extension of the State Space

中文关键词:  超布朗运动  质量过程  分布弱收敛  值空间

英文关键词:super-Brownian motion  mass process  distributional weak convergence  state space

中文摘要:

      本文给出了超布朗运动的质量过程在不灭绝条件下的极限分布的拉普拉斯变换的具体形式，并得出了在较一般的分支特征下使其值空间从M_F（R^d）扩张到M_P（R^d）的一个充分条件．

英文摘要:

      Under non-extinction conditions , we study the limiting behaviour 0f the mass process of the super-Brownian motion and give the clear formulation of the Laplace transformation of the limiting distribution. In the last part of the paper we give a sufficient condition under which the state space of the super-Brownian motion with a more general branching mechanism can be extended from M_F（R^d） to M_P（R^d）.