Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems

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Derivative formula and applications for degenerate diffusion semigroups (2011, background): “[3, 15] where some long time behaviors of the system have been investigated.”
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré (2007, methodology): “It turns out that this model enters the framework of Meyn-Tweedie approach as shown in [35] (also see [9]).”
Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes (2005, background): “In a similar vein, in [44] the following condition is imposed for a diffusion on X = Rn: For any n ≥ 1 there exists Kn ⊂ X compact, such that for any compact set K ⊂ X, sup x∈K Ex[eKn ] <∞.”
Exponential Stability of Slowly Decaying Solutions to the Kinetic-Fokker-Planck Equation (2014, background): “Let us mention that there is an important literature in the probability community, see for instance [25, 3], that deals with exponential relaxation to equilibrium for stochastic processes whose law follows kinetic Fokker-Planck equations.”
Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations (2014, unknown): “We refer for instance to [29, 37, 50, 56].”
Couplings and quantitative contraction rates for Langevin dynamics (2017, methodology): “The choice of the Lyapunov function is motivated by Mattingly, Stuart and Higham [32], see also [39, 46, 1].”