Transition Semigroups of Banach Space-Valued Ornstein–Uhlenbeck Processes

By B. Goldys, J. V. Neerven. 2003

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We investigate the transition semigroup of the solution to a stochastic evolution equation dX(t)=AX(t) dt+dWH(t), t≥0, where A is the generator of a C0-semigroup S on a separable real Banach space E and WH(t)t≥0 is cylindrical white noise with values in a real Hilbert space H which is continuously embedded in E. Various properties of these semigroups, such as the strong Feller property, the spectral gap property, and analyticity, are characterized in terms of the behaviour of S in H. In particular we investigate the interplay between analyticity of the transition semigroup, S-invariance of H, and analyticity of the restricted semigroup SH.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/8870b2dd421d5f01bac03f81a1c1cb508e39786f