Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration

Details Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration

2006-06-24

arxiv.org/abs/math/0606619v1

Potential Analysis 21 (2004), 1: 75-97

Mathematics

Probability

Scientific paper

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 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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