Large deviations for stochastic processes on Riemannian manifolds

This thesis is concerned with large deviations for processes in Riemannian manifolds. In particular, we study the extensions of large deviations for random walks and Brownian motion to the geometric setting. Furthermore, we also consider large deviations for random walks in Lie groups. The additional group structure allows for improvements over the general case. Finally, we also study large deviations for Brownian motion in evolving Riemannian manifolds. For this, we use the so-called 'rolling without slipping' construction of Riemannian Brownian motion, adepted to the time-inhomogeneous setting.