| 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. |
