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We consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is known to fulfil a…

Probability · Mathematics 2011-11-23 Radosław Adamczak , Piotr Miłoś

We study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an Ornstein-Uhlenbeck noise. This system undergoes a noise-induced bifurcation when the amplitude of the noise…

Statistical Mechanics · Physics 2014-12-19 Kirone Mallick , Pierre-Emmanuel Peyneau

It is considered Ornstein-Uhlenbeck process $ x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s$, where $x_0 \in R$, $\theta>0$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k…

Statistics Theory · Mathematics 2016-08-30 Levan Labadze , Gogi Pantsulaia

The fractional Ornstein-Uhleneck (fOU) process is described by the overdamped Langevin equation $\dot{x}(t)+\gamma x=\sqrt{2 D}\xi(t)$, where $\xi(t)$ is the fractional Gaussian noise with the Hurst exponent $0<H<1$. For $H\neq 1/2$ the fOU…

Statistical Mechanics · Physics 2025-03-03 Alexander Valov , Baruch Meerson

We provide a comprehensive analysis of the positional dynamics and average thermodynamics of an overdamped Brownian particle subject to both, harmonic confinement and annealed disorder due to a temporarily fluctuating trap stiffness. We…

Statistical Mechanics · Physics 2025-09-17 Deepak Gupta , Sabine H. L. Klapp

In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the…

Soft Condensed Matter · Physics 2020-01-08 Helmut H. Strey

In this paper, we derive closed-form expressions for significant statistical properties of the link signal-to-noise ratio (SNR) and the separation distance in mobile ad hoc networks subject to Ornstein-Uhlenbeck (OU) mobility and Rayleigh…

Dynamical Systems · Mathematics 2019-12-23 Arta Cika , Mihai-Alin Badiu , Justin P. Coon

In this paper we study the linear and nonlinear Schr\"odinger equations associated with the Ornstein-Uhlenbeck (OU) operator endowed with the Gaussian measure. While classical Strichartz estimates are well-developed for the free…

Functional Analysis · Mathematics 2025-07-08 Aparajita Dasgupta , Uttam Kumar Dolai , Cheng Luo , Manli Song

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 a Ornstein-Uhlenbeck process, supplemented…

Fluid Dynamics · Physics 2017-09-26 Laurent Chevillard

Recently, interesting data concerning $dN_{ch}/d\eta$ in Au-Au collisions [$\eta=-\ln \tan (\theta/2)$] with centrality cuts have been reported from the PHOBOS Collaboration. In most treatment these data are divided by the number of…

Nuclear Theory · Physics 2009-11-07 M. Biyajima , M. Ide , T. Mizoguchi , N. Suzuki

This paper studies one-dimensional Ornstein-Uhlenbeck processes, with the distinguishing feature that they are reflected on a single boundary (put at level 0) or two boundaries (put at levels 0 and d>0). In the literature they are referred…

Probability · Mathematics 2014-07-03 Gang Huang , Michel Mandjes , Peter Spreij

In this paper we consider an Ornstein-Uhlenbeck (OU) process $(M(t))_{t\geqslant 0}$ whose parameters are determined by an external Markov process $(X(t))_{t\geqslant 0}$ on a finite state space $\{1,\ldots,d\}$; this process is usually…

Probability · Mathematics 2024-06-06 Gang Huang , Marijn Jansen , Michel Mandjes , Peter Spreij , Koen De Turck

Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate…

Statistical Finance · Quantitative Finance 2026-05-19 Ranieri Dugo , Giacomo Giorgio , Paolo Pigato

We consider the problem of modelling restricted interactions between continuously-observed time series as given by a known static graph (or network) structure. For this purpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck…

Statistics Theory · Mathematics 2021-07-08 Valentin Courgeau , Almut E. D. Veraart

In stochastic population dynamics, stochastic wandering can produce transition to an absorbing state. In particular, under Allee effects, low densities amplify the possibility of population collapse. We investigate this in an…

Populations and Evolution · Quantitative Biology 2026-01-13 Luis F. Gordillo , Priscilla E. Greenwood

We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…

Machine Learning · Statistics 2026-02-04 Stephen Y. Zhang , Michael P H Stumpf

We consider the anomalous sub-diffusion of a class of Gaussian processes that can be expressed in terms of sums of Ornstein-Uhlenbeck processes. As a generic class of processes, we introduce a single parameter such that for any $\nu \in…

Probability · Mathematics 2009-11-24 Scott A McKinley

Learning is a fundamental property of intelligent systems, observed across biological organisms and engineered systems. While modern intelligent systems typically rely on gradient descent for learning, the need for exact gradients and…

Machine Learning · Computer Science 2024-12-10 Jesus Garcia Fernandez , Nasir Ahmad , Marcel van Gerven

Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of…

Machine Learning · Statistics 2017-07-12 Stéphane Gaïffas , Gustaw Matulewicz

In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…

Probability · Mathematics 2015-08-12 Pierre-A. Vuillermot , Jean-C. Zambrini