On the Theory of the Brownian Motion

By G. Uhlenbeck, L. Ornstein. 1930

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In Pure Mathematics

Citations in the corpus

Reinforcement learning (2019, neutral): “In line 7 of algorithm 2, the action to take given the state s is generated as where ϵ is generated from an Uhlenbeck-Ornstein process (Uhlenbeck and Ornstein, 1930) (noise is correlated between each learning step in algorithm 2).”
Input Convex Neural Networks (2016, methodology): “quired to be positive). In our experiments training ICNNs for Q learning, we also use replay memory [Lin, 1993], gradient and reward clipping [Mnih et al., 2013], and exploration with the OU process [Uhlenbeck and Ornstein, 1930]. Algorithm 3 gives a complete description of deep Q-learning with ICNN”
A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties (2006, unknown): “The Ornstein–Uhlenbeck model (Uhlenbeck and Ornstein 1930) provides a good description of inhomogeneous stochastic synaptic input (Tuckwell 1989), τ dv(t) dt = −[v(t) − V0] + µ(t) + σ(t) √ 2τ ξ(t) , (7) where ξ(t) is Gaussian white noise, and the drift µ(t) and variance σ(t) of the input can both…”
Modeling irregularly spaced residual series as a continuous stochastic process (2005, methodology): “[17] A comparison of the AR(1) model, conventional or embedded in a Kalman filter, and the Ornstein-Uhlenbeck– based noise model shows that their equations for respectively the forecasting mode in the AR(1) model, those handling the predictions and their variance in the time update of the degenerate”
Complex (dusty) plasmas: current status, open issues, perspectives (2005, background): “Charge fluctuations due to discrete nature of charging can be described as a stationary, Gaussian and Markovian process (or the Ornstein–Uhlenbeck process [131]).”
Safe, Efficient, and Comfortable Velocity Control based on Reinforcement Learning for Autonomous Driving (2019, methodology): “[9], an Ornstein-Uhlenbeck process [23] with θ = 0.”
Fractional Ornstein-Uhlenbeck processes (2003, background): “Uhlenbeck and Ornstein (1930) imposed probability hypotheses on F (t) and then derived that for v(0) = x ∈ R, v(t) is normally distributed with mean xe−λt and variance σ 2 2λ ( 1− e−2λt ) , for λ = f m and σ2 = 2fkT m2 , where k is the Boltzmann constant and T the temperature.”
A Recurrent Network Mechanism of Time Integration in Perceptual Decisions (2006, unknown): “This is thus described by an Ornstein–Uhlenbeck process (Uhlenbeck and Ornstein, 1930) (for example, see Destexhe et al., 2001): ␶ AMPA dI noise ͑t͒ dt ϭ ϪI noise ͑t͒ ϩ ␩͑t͒ ͱ␶ AMPA ␴ noise 2 , where ␴ noise 2 is the variance of the noise, and ␩ is a Gaussian white noise with zero mean and unit…”
Understanding fine magnetic particle systems through use of first‐order reversal curve diagrams (2014, methodology): “By treating bulk samples as statistical ensembles of grains with Gaussian volume distributions and an Ornstein-Uhlembeck random process [Uhlenbeck and Ornstein, 1930] to generate a pinning field in each grain, Pike et al. [2001b] ROBERTS ET AL.”