Non-differentiable Skew Convolution Semigroups and Related Ornstein-Uhlenbeck Processes

Donald A. Dawson; Zenghu Li

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arXiv · math/0606620

Non-differentiable Skew Convolution Semigroups and Related Ornstein-Uhlenbeck Processes

Donald A. Dawson·Zenghu Li

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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.

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BibTeX RIS

Donald A. Dawson, Zenghu Li. 2006-06-24. Non-differentiable Skew Convolution Semigroups and Related Ornstein-Uhlenbeck Processes. https://arxiv.org/abs/math/0606620

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