Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration
Probability
2007-05-23 v1
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 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.
Keywords
Cite
@article{arxiv.math/0606619,
title = {Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration},
author = {Donald A. Dawson and Zenghu Li and Byron Schmuland and Wei Sun},
journal= {arXiv preprint arXiv:math/0606619},
year = {2007}
}