Non-differentiable Skew Convolution Semigroups and Related Ornstein-Uhlenbeck Processes
Probability
2011-02-19 v1
Abstract
It is proved that a general non-differentiable skew convolution semigroup associated with a strongly continuous semigroup of linear operators on a real separable Hilbert space can be extended to a differentiable one on the entrance space of the linear semigroup. A cadlag strong Markov process on an enlargement of the entrance space is constructed from which we obtain a realization of the corresponding Ornstein-Uhlenbeck process. Some explicit characterizations of the entrance spaces for special linear semigroups are given.
Cite
@article{arxiv.math/0606620,
title = {Non-differentiable Skew Convolution Semigroups and Related Ornstein-Uhlenbeck Processes},
author = {Donald A. Dawson and Zenghu Li},
journal= {arXiv preprint arXiv:math/0606620},
year = {2011}
}