Lower order perturbations of Dirichlet processes
Michael Röckner, T. S. Zhang · Forum Mathematicum · 2003
We consider lower order perturbations M of symmetric diffusions M-0 and prove that M is locally absolutely continuous with respect to M-0 up to life time. The novelty is that the absolute value of the drift b and zero order part c are merely assumed to be in L-d (R-d) + L-infinity(R-d), and Ld/2(R-d)+L-infinity(R-d). So, \\b\\(2) and c are not in the Kato-class (as is the case when \\b\\(2), \\c\\ is an element of L-p(R-d) + L-infinity(R-d) with p > d/2). We also consider the case where an adjoint drift is present. Finally, we use these results to prove new convergence results for diffusions.