Approach to Markovianity for random motions on hyperbolic spaces and time inhomogeneous jump processes

The object of this thesis are jump-type Markov processes. On the one hand, we study random flights on manifolds: a motion among random obstacles on a hyperbolic space, together with its Boltzmann-Grad limit, is analysed. On the other hand, we use tools regarding Levy processes and subordinators: additive increasing processes, called inhomogeneous subordinators, are used to extend the theory of Bochner subordination.