Stochastic analysis in a tubular neighborhood or Onsager-Machlup   functions revisited
  Yet another proof of Onsager-Machlup formula for diffusion processes on a Riemannian manifold after Takahashi-Watanabe, Fujita-Kotani. The proof is purely probabilistic and contains a precise study on an ergodic effect for a key Wiener functional. 
Keisuke Hara and Yoichiro Takahashi
math.PR