  Limit theorems are presented for the rescaled occupation time fluctuation
process of a critical finite variance branching particle system in
$\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either
a standard Poisson random field or the equilibrium distribution for critical
$d=2\alpha$ and large $d>2\alpha$ dimensions. The limit processes are
generalised Wiener processes. The obtained convergence is in space-time,
finite-dimensional distributions sense. With the addtional assumption on the
branching law we obtain functional convergence.
