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

Abstract:

      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）.