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

Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions