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We establish fluctuation limit theorems of immigration superprocesses with small branching rates. The weak convergence of the processes on a Sobolev space is established, which improves the result of Gorostiza and Li (High density fluctuations of immigration branching particle systems. In: Gorostiza, L.G., Ivanoff, B.G. (Eds.), Stochastic Models, (Ottawa, Ontario, 1998), CMS Conference Proceedings...
Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein–Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on a real separable Hilbert space whose characteristic functional is not necessarily differentiable at the initial time. A connection between this subject and catalytic branching superprocesses is established...
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