Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in ${\mathbb{R}}^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.