  This paper proposes additional material to the main statements of [HL13]
which are are recalled in Section~2. In particular an application of
[Theorem~2.2,HL13] to Renewal Markov Processes is provided in Section~4 and a
detailed checking of the assumptions of [Theorem~2.2,HL13] for the joint
distribution of local times of a finite jump process is reported in Section~5.
A uniform version of [Theorem~2.2,HL13] with respect to a compact set of
transition matrices is given in Section~6 (see [Remark 2.4,HL13]). The basic
material on the semigroup of Fourier matrices and the spectral approach used in
[HL13] is recalled in Section~3 in order to obtain a good understanding of the
properties involved in this uniform version.
