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 through fluctuation limits, providing a rich class of non-differentiable skew convolution semigroups. Path regularity of the corresponding generalized Ornstein-Uhlenbeck processes in different topologies is also discussed.

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Keywords catalytic branching superprocess, fluctuation limit, generalized Mehler semigroup, immigration, Ornstein-Uhlenbeck process, skew convolution semigroup
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Journal Potential Analysis
Dawson, D.A, Li, Z. (Zenghu), Schmuland, B. (Byron), & Sun, W. (Wei). (2004). Generalized Mehler semigroups and catalytic branching processes with immigration. Potential Analysis, 21(1), 75–97. doi:10.1023/B:POTA.0000021337.13730.8c