Perturbation of non-symmetric Dirichlet forms and associated Markov processes (Q2746529)

A quasi-regular Dirichlet form \((\mathcal E,D(\mathcal E))\) on a metrisable Lusin space with a \(\sigma\) finite Borel measure \(m\) perturbed by a smooth signed measure \(\mu =\mu-\mu^{-}\) is studied, where \(\mu\) is smooth and \(\mu^{-}\) is in Kato class. The perturbed form \((\mathcal E^{\mu},D(\mathcal E^{\mu}))\) is proved to be \(h\)-associated with an \(m\)-tight \(m\)-special standard process by extending the necessary and sufficient condition of a strongly contract Markovian semigroup associated with a Markov process to a strongly uniformly bounded Markovian semigroup.