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

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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.
Classification : 47D07, 60J35
Mots-clés : semigroup acting on real-valued functions defined in a Hilbert space, transition semigroup, stochastic process, Gaussian measure, bilinear closed coercive form, closability criterion 
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     title = {Analyticity of transition semigroups and closability of bilinear forms in {Hilbert} spaces},
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     volume = {115},
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     zbl = {0830.47033},
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Marco Fuhrman. Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces. Studia Mathematica, Tome 115 (1995) no. 1, p. 53. https://geodesic-test.mathdoc.fr/item/STUMA_1995__115_1_216198/