Ornstein–Uhlenbeck process ≈ Ornstein–Uhlenbeck process
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Statistical mechanics of active Ornstein-Uhlenbeck particles Open
We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this s…
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Environmental variability and mean-reverting processes Open
Environmental variability is often incorporated in a mathematical model by modifying the parameters in the model. In the present investigation, two common methods to incorporate the effects of environmental variability in stochastic differ…
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The entropy production of Ornstein–Uhlenbeck active particles: a path integral method for correlations Open
By employing a path integral formulation, we obtain the entropy production\nrate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the\npresence and in the absence of thermal noise. The present treatment clarifies\nsome co…
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Active Ornstein-Uhlenbeck particles Open
Active Ornstein-Uhlenbeck particles (AOUPs) are overdamped particles in an interaction potential subject to external Ornstein-Uhlenbeck noises. They can be transformed into a system of underdamped particles under additional velocity depend…
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Symmetric exclusion process under stochastic resetting Open
We study the behavior of a symmetric exclusion process (SEP) in the presence of stochastic resetting where the configuration of the system is reset to a steplike profile with a fixed rate r. We show that the presence of resetting affects b…
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Beyond Brownian Motion and the Ornstein-Uhlenbeck Process: Stochastic Diffusion Models for the Evolution of Quantitative Characters Open
Gaussian processes, such as Brownian motion and the Ornstein-Uhlenbeck process, have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks that li…
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Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model Open
In this paper, we propose a multilevel process modeling approach to describing individual differences in within-person changes over time. To characterize changes within an individual, repeated measures over time are modeled in terms of thr…
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Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit Open
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small …
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Generalized Ornstein-Uhlenbeck model for active motion Open
We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming vel…
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Approximate Bayes learning of stochastic differential equations Open
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions, a…
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Extremal statistics for stochastic resetting systems Open
While averages and typical fluctuations often play a major role in understanding the behavior of a nonequilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of …
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Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise Open
A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck\nnoise $\\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\\eta$\nis described by a Markov process in two dimensions. But even though there\nexist…
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Convergence of transport noise to Ornstein–Uhlenbeck for 2D Euler equations under the enstrophy measure Open
We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that stationary solutions of this equation converge to the unique stationary …
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Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process Open
In this paper, we solve the Fokker–Planck equation of the multivariate Ornstein–Uhlenbeck process to obtain its probability density function. This approach allows us to ascertain the distribution without solving it analytically. We find th…
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A Cautionary Note on “A Cautionary Note on the Use of Ornstein Uhlenbeck Models in Macroevolutionary Studies” Open
Models based on the Ornstein–Uhlenbeck process have become standard for the comparative study of adaptation. Cooper et al. (2016) have cast doubt on this practice by claiming statistical problems with fitting Ornstein–Uhlenbeck models to c…
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Modeling Interdependent Animal Movement in Continuous Time Open
Summary This article presents a new approach to modeling group animal movement in continuous time. The movement of a group of animals is modeled as a multivariate Ornstein Uhlenbeck diffusion process in a high-dimensional space. Each indiv…
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Fast Bayesian inference of the multivariate Ornstein-Uhlenbeck process Open
The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an O(N) Bayesian method to estimate the drift and diffusion matr…
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Characterising the nonequilibrium stationary states of Ornstein–Uhlenbeck processes Open
We characterise the nonequilibrium stationary state of a generic multivariate\nOrnstein-Uhlenbeck process involving $N$ degrees of freedom. The\nirreversibility of the process is encoded in the antisymmetric part of the\nOnsager matrix. Th…
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Irreversibility in Active Matter: General Framework for Active Ornstein-Uhlenbeck Particles Open
Active matter systems are driven out of equilibrium by conversion of energy into directed motion locally on the level of the individual constituents. In the spirit of a minimal description, active matter is often modeled by so-called activ…
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Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity Open
We study the relaxation behavior of the Ornstein-Uhlenbeck (OU) process with time-dependent and fluctuating diffusivity. In this process, the dynamics of the position vector is modeled by the Langevin equation with a linear restoring force…
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Ornstein-Uhlenbeck Processes Driven by Cylindrical Lévy Processes Open
In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical Lévy processes in separable Banach spaces. Here, a cylindrical Lévy process is understood in the classical frame…
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Markov-modulated Ornstein–Uhlenbeck processes Open
In this paper we consider an Ornstein–Uhlenbeck (OU) process ( M ( t )) t ≥0 whose parameters are determined by an external Markov process ( X ( t )) t ≥0 on a finite state space {1, . . ., d }; this process is usually referred to as Marko…
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Regularized fractional Ornstein-Uhlenbeck processes and their relevance to the modeling of fluid turbulence Open
Motivated by the modeling of the temporal structure of the velocity field in a highly turbulent flow, we propose and study a linear stochastic differential equation that involves the ingredients of an Ornstein-Uhlenbeck process, supplement…
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Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes Open
We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by Lévy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential equations,…
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An application of Ornstein-Uhlenbeck process to commodity pricing in Thailand Open
In this paper, we examine an application of Ornstein-Uhlenbeck process to commodity pricing in Thailand. Prices of Tapioca Starch, Ribbed Smoke Sheet no. 3, and Thai Hom Mali Rice are investigated. We use three parameter estimation methods…
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Comparing Information Metrics for a Coupled Ornstein–Uhlenbeck Process Open
It is often the case when studying complex dynamical systems that a statistical formulation can provide the greatest insight into the underlying dynamics. When discussing the behavior of such a system which is evolving in time, it is usefu…
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Consistency of the drift parameter estimator for the discretized fractional Ornstein–Uhlenbeck process with Hurst index H ∈ (0, 12) Open
parameter θ and where the noise is modeled as fractional Brownian motionwith Hurst index H ∈ (0, 12 ). The solution corresponds to the fractionalOrnstein–Uhlenbeck process. We construct an estimator, based on discreteobservations in time, …
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Implications of the Ornstein-Uhlenbeck-like fractional differential equation in cosmology Open
"In this paper we introduce a generalized fractional scale factor and a time-dependent Hubble parameter obeying an “Ornstein-Uhlenbeck-likefractional differential equation” which serves to describe the accelerated expansion of a non-singul…
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Large deviations for the Ornstein-Uhlenbeck process with shift Open
We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformat…
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Fast shuttling of a particle under weak spring-constant noise of the moving trap Open
We investigate the excitation of a quantum particle shuttled in a harmonic trapwith weak spring-constant colored noise. The Ornstein-Uhlenbeck model for the noise correlation function describes a wide range of possible noises, in particula…