A transformation of a symmetric Markov process and the Donsker-Varadhan theory (Q795407)

It is considered an m-symmetric Hunt process \(M=(X_ t,P_ x,\zeta)\) on a locally compact separable metric space X with a positive Radon measure m. The Beurling-Deny formulas are derived for the Dirichlet forms corresponding to the process M and the conservative process \(\tilde M\) obtained from M by a transformation of probability measures \(P_{\alpha}\) using defined local densities. By means of these results a lower bound is obtained for the Donsker-Varadhan law of large deviation of the occupation distribution for the process M.