Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration
نویسندگان
چکیده
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 nondifferentiable skew convolution semigroups. Path regularity of the corresponding generalized Ornstein-Uhlenbeck processes in different topologies is also discussed. Mathematics Subject Classifications (2000): Primary 60J35, 60G20; Secondary 60G57, 60J80
منابع مشابه
DLSS (2001/03/15) Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration
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 gi...
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