Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces
Volume 115 / 1995
Studia Mathematica 115 (1995), 53-71
DOI: 10.4064/sm-115-1-53-71
Abstract
We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the $L^2(μ)$ space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in $L^2(μ)$. A closability criterion for such forms is presented. Examples are also given.
