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 càdlàg 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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Dawson, D.A., Li, Z. Non-Differentiable Skew Convolution Semigroups and Related Ornstein–Uhlenbeck Processes. Potential Analysis 20, 285–302 (2004). https://doi.org/10.1023/B:POTA.0000010666.75722.0e
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DOI: https://doi.org/10.1023/B:POTA.0000010666.75722.0e