On the theory of brownian motion

By R. Mazo. 1973

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Citations in the corpus

Continuous control with deep reinforcement learning (2015, methodology): “As detailed in the supplementary materials we used an Ornstein-Uhlenbeck process [10] to generate temporally correlated exploration (similar use of autocorrelated noise for efficient exploration was introduced in [11]).”
Addressing Function Approximation Error in Actor-Critic Methods (2018, methodology): “Unlike the original implementation of DDPG, we used un-correlated noise for exploration as we found noise drawn from the Ornstein-Uhlenbeck (Uhlenbeck & Ornstein, 1930) process offered no performance beneﬁts.”
Reinforcement Learning with Deep Energy-Based Policies (2017, neutral): “(Uhlenbeck & Ornstein, 1930; Lillicrap et al., 2015) to improve exploration.”
Distributed Prioritized Experience Replay (2018, methodology): “Unlike the original DPG algorithm which applies autocorrelated noise sampled from a OrnsteinUhlenbeck process (Uhlenbeck & Ornstein (1930)), we apply exploration noise to each action sampled from a normal distribution with σ = 0.3.”
Learning to Drive in a Day (2018, methodology): “We use a standard method of achieving this in the context of continuous reinforcement learning methods: our exploration policy is formed by adding discrete Ornstein-Uhlenbeck process noise [32] to the optimal policy.”
Distributed Distributional Deterministic Policy Gradients (2018, neutral): “025 ˝ , θ =0.01; Uhlenbeck & Ornstein 1930).”
Stochastic Gradient Descent as Approximate Bayesian Inference (2017, methodology): “The four assumptions above result in a speciﬁc kind of stochastic process, the multivariate Ornstein-Uhlenbeck process (Uhlenbeck and Ornstein, 1930).”
Parameter Space Noise for Exploration (2017, background): “2 ), (c) correlated additive Gaussian action space noise (Ornstein–Uhlenbeck process [17] with σ = 0 .”
Entropy Search for Information-Efficient Global Optimization (2011, background): “Other kernels can be used to induce beliefs over non-smooth functions (Mat´ern, 1960), and even over non-continuous functions (Uhlenbeck and Ornstein, 1930).”
Gaussian Process Regression Networks (2011, methodology): “The Ornstein-Uhlenbeck kernel is also widely applied: In one dimension it is the covariance function of an Ornstein-Uhlenbeck process (Uhlenback and Ornstein, 1930), which was introduced to model the velocity of a particle undergoing Brownian motion.”
A Variational Analysis of Stochastic Gradient Algorithms (2016, methodology): “Based on its interpretation as a continuous-time stochastic process—speciﬁcally a multivariate Ornstein-Uhlenbeck (OU) process (Uhlenbeck and Ornstein, 1930; Gardiner et al., 1985)—we compute stationary distributions for a large class of SGD algorithms, all of which converge to a Gaussian…”
Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms (2015, methodology): “This is the well-known Ornstein-Uhlenbeck process Uhlenbeck & Ornstein (1930), which is exactly solvable (see SM. B.3), yielding the Gaussian distribution X t ∼ N ( x 0 e − 2(1+ η ) t , η 1+ η (1 − e − 4(1+ η ) t )) .”
Drift estimation for a periodic mean reversion process (2010, methodology): “Combining the assumption of periodicity with the parametric model (2) leads to the requirement (9) φj(t+ ν) = φj(t).”
ctmm: an r package for analyzing animal relocation data as a continuous‐time stochastic process (2016, methodology): “The Ornstein – Uhlenbeck (OU) process combines BM with a tendency to remain in a particular area (Uhlenbeck & Ornstein 1930; Dunn & Gipson 1977).”
Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, methodology): “The O-U process Oδ is also called a colored noise because its power spectrum is not flat compared to the white noise, see for instance [4, 25, 42, 43, 55].”
Swarming, schooling, milling: phase diagram of a data-driven fish school model (2013, background): “This led to the representation of single fish behaviour as a two-dimensional smooth random walk in which an Ornstein–Uhlenbeck process [20] acts on the fish angular velocity ω.”
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].”