Path integrals for diffusion processes in Riemannian spaces

The Onsager-Machlup lagrangian for general continuous Markov processes in curved spaces will be derived invoking (i) continuous and differentiable trajectories, (ii) a Fourier series analysis of stochastic paths and (iii) the principle of general covariance. No discretization rule will be required in order to put the continuous action on a lattice. (Auth.)