On the semi-group of a scaled skew Bessel process

We define scaled skew Bessel processes and determine their Green's functions and semi-group densities. We prove that these processes satisfy the time inversion property although the corresponding densities of the semi-groups are not, in general, twice differentiable in the density and starting point arguments. Some characterizations and semi-martingale properties are given. Crown Copyright (C) 2018 Published by Elsevier B.V. All rights reserved.