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

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

2006-06-24

arxiv.org/abs/math/0606620v1

Potential Analysis 20 (2004), 285-302

Mathematics

Probability

Scientific paper

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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