Uniqueness of Nelson's diffusions. II: Infinite dimensional setting and applications
[For part I see Probab. Theory Relat. Fields 114, No. 4, 549-585 (1999; Zbl 0936.60072).] It is proved that the generalized Schrödinger operator \({\mathcal L}^\varphi={\mathcal L}+ 2\Gamma(\varphi,\cdot)/\varphi\) generates a unique \(C_0\)-semigroup in \(L'\). Here \({\mathcal L}\) is the generator of a diffusion and \(\Gamma\) is the carré-du-champs operator of Meyer: \(2\Gamma(f,g)={\mathcal L}(fg)- f{\mathcal L}g- ({\mathcal L}f)g\), \(f,g\in {\mathcal D}({\mathcal L})\).
scientific article; zbMATH DE number 1569537