DLSS (2001/03/15) Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration
نویسندگان
چکیده
A generalized Mehler semigroup (Ornstein-Uhlenbeck semigroup) associated with some strongly continuous semigroup of linear operators on a real separable Hilbert space may be defined by using a skew convolution semigroup. Under a mild moment assumption, it is proved that the characteristic functional of any centered skew convolution semigroup is absolutely continuous and characterizations are given for centered skew convolution semigroups whose characteristic functionals are not necessarily differentiable at the initial time. A connection between the subject and measure-valued catalytic branching processes is established by using fluctuation limits of their associated immigration processes. Path regularity of the generalized the corresponding Ornstein-Uhlenbeck processes in different topologies is also discussed.
منابع مشابه
Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration
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 est...
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