A quenched CLT for super-Brownian motion with random immigration

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A quenched central limit theorem is derived for the super-Brownian motion with super-Brownian immigration, in dimension $d\geq 4$. At the critical dimension $d=4$, the quenched and annealed fluctuations are of the same order but are not equal.
A small mistake in the proof of Proposition 2.2 is corrected, and typos removed

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