Conze, J.-P.; Le Borgne, S. Martingale method and geodesic flow on a surface of constant negative curvature. (Méthode de martingales et flot géodésique sur une surface de courbure constante négative.) (French) Zbl 0983.37034 Ergodic Theory Dyn. Syst. 21, No. 2, 421-441 (2001). Authors’ abstract: Let \(({\mathcal T}^1S, m,(T^t)_{t\in\mathbb{R}})\) be the geodesic flow on the unit tangent bundle of a surface \(S\) of negative constant curvature and finite volume. We show that every Hölder function on \({\mathcal T}^1S\) is, for the discrete time action of the geodesic flow, homologous to a martingale increment. From this representation follow the central limit theorem and its improvements, and a characterization of Hölder functions which are coboundaries in the class of measurable functions. Reviewer: Simon Eloshvili (Tbilisi) Cited in 15 Documents MSC: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 58J65 Diffusion processes and stochastic analysis on manifolds 60G42 Martingales with discrete parameter Keywords:martingale method; geodesic flow; tangent bundle PDFBibTeX XMLCite \textit{J. P. Conze} and \textit{S. Le Borgne}, Ergodic Theory Dyn. Syst. 21, No. 2, 421--441 (2001; Zbl 0983.37034) Full Text: DOI