广义Mehler半群与带迁移的催化分支过程
Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration
摘要：
斜卷积半群在广义Mehler半群和Ornstein-Uhlenbeck过程的研究中起着重要的作用。给出了实可分希尔伯特空间上特征泛函在初始时刻不一定可微的一般斜卷积半群的一个刻划.这个主题和催化分支超过程之间的联系是通过波动极限建立的，提供了一类丰富的不可微斜卷积半群。讨论了相应的广义Ornstein-Uhlenbeck过程在不同拓扑下的路径正则性。
英文摘要：
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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