On the Theory of the Brownian Motion II

By M. Wang, G. Uhlenbeck. 1945

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Stochastic Gradient Hamiltonian Monte Carlo (2014, methodology): “Importantly, we note that the Langevin dynamics used in SGLD (Welling and Teh, 2011) are ﬁrst-order, which can be viewed as a limiting case of our second-order dynamics when the friction term is large.”
Harmonicity in slow protein dynamics (2000, methodology): “The corresponding stochastic process described by it is known as the Ornstein±Uhlenbeck process [8].”
Relativistic Brownian Motion (2008, background): “The brief summary of nonrelativistic Brownian motion theory in the preceding section shows that equilibrium thermostatistics plays an important role in constraining the relation between friction and noise coefficients in Langevin equations by means of suitably chosen fluctuation-dissipation…”
Brownian Motion in AdS/CFT (2008, unknown): “One of the most useful playgrounds for understanding the quantum behavior of black holes has been the (1)Classic reviews on Brownian motion are [2, 3, 4].”
Mechanics of biomolecules (2002, methodology): “(14b) should be used in this case according to the ;uctuation–dissipation relation (Uhlenbeck and Ornstein, 1930; Wang and Uhlenbeck, 1945; Fox, 1978).”
Interacting Particle Solutions of Fokker–Planck Equations Through Gradient–Log–Density Estimation (2020, methodology): “Indispensable tools for the analysis of stochastic systems are Kolmogorov equations, and in particular the Fokker–Planck equation (FPE) [21,22].”