Abstract
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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Dawson, D.A., Li, Z., Schmuland, B. et al. Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration. Potential Analysis 21, 75–97 (2004). https://doi.org/10.1023/B:POTA.0000021337.13730.8c
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DOI: https://doi.org/10.1023/B:POTA.0000021337.13730.8c