On the perturbation problem for occupation densities (Q1315399)

Let \(X\) be a continuous semimartingale. There is considered \(X\) perturbed by a process \(V\) possibly anticipating. If \(V\) is not adapted, the process \(X+V\) is not a semimartingale. But under some smoothness conditions on \(V\) it is proved that \(X+V\) possesses the occupation densities \(L(V,.,.)\). There are given sufficient conditions for the continuity of the obtained occupation densities \(L(V,y,t)\) in \((y,t)\). They are the same as in the classical case of martingales perturbed by an adapted process of bounded variation.