Geodesic
Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces
Studia Mathematica, Tome 115 (1995) no. 1, pp. 53-71

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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. 
Marco Fuhrman. Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces. Studia Mathematica, Tome 115 (1995) no. 1, pp. 53-71. doi: 10.4064/sm-115-1-53-71
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