Feynman-Kac functional and the Schrödinger equation.- Two results on dual excursions.- Characterization of Lévy measures of inverse local times of gap diffusion.- Lévy systems and path decompositions.- Regular birth and death times.- Some results on energy.- Absolute continuity and the fine topology.- Representation of semimartingale Markov processes in terms of Wiener processes and Poisson random measures.