Larbi Alili

We prove that a space inversion property of a standard Markov process X implies the existence of a Kelvin transform of X-harmonic, excessive and operator–harmonic functions and that the inversion property is inherited by Doob h-transforms. We determine new classes of processes having space inversion properties amongst those satisfying the time inversion property. For these processes, some explicit inversions, which are often not the spherical ones, and excessive functions are given explicitly. Some examples are treated in details.