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Related papers: The Elliptical Ornstein-Uhlenbeck Process

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In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…

Dynamical Systems · Mathematics 2024-01-17 Tomás Caraballo , Renato Colucci , Javier López-de-la-Cruz , Alain Rapaport

Using a mixture of classical and probabilistic techniques we investigate the convexity of solutions to the elliptic pde associated with a certain generalized Ornstein-Uhlenbeck process.

Analysis of PDEs · Mathematics 2014-07-16 Jon Warren

The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. When structural changes happen,…

Methodology · Statistics 2017-05-30 Fuqi Chen , Rogemar Mamon , Matt Davison

Lognormality was found experimentally for coarse-grained squared turbulence velocity and velocity increment when the coarsening scale is comparable to the correlation scale of the velocity (Mouri et al. Phys. Fluids 21, 065107, 2009). We…

Chaotic Dynamics · Physics 2013-01-29 Takeshi Matsumoto , Masanori Takaoka

Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity…

Neurons and Cognition · Quantitative Biology 2026-01-30 P. O. Michel , C. Sun , S. Jaffard , D. Longrois , D. Holcman

We consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypoelliptic diffusion processes on finite-dimensional Lie groups: let $ \mathcal{L} $ be a hypoelliptic, left-invariant ``sum of the squares''-operator on a Lie group $…

Probability · Mathematics 2008-05-12 Fabrice Baudoin , Martin Hairer , Josef Teichmann

L\'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current…

Computational Finance · Quantitative Finance 2026-05-07 Roberto Baviera , Pietro Manzoni

We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean…

Trading and Market Microstructure · Quantitative Finance 2024-12-18 Jirat Suchato , Sean Wiryadi , Danran Chen , Ava Zhao , Michael Yue

We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein-Uhlenbeck process with Levy noise and bounded drift. We…

Probability · Mathematics 2015-06-25 Fred Espen Benth , Barbara Ruediger , Andre Suess

We derive an explicit representation for the transition law of a $p$-tempered $\alpha$-stable process of Ornstein-Uhlenbeck-type and use it to develop a methodology for simulation. Our results apply in both the univariate and multivariate…

Probability · Mathematics 2020-05-20 Michael Grabchak

Standard Ornstein-Uhlenbeck (OU) models often yield biased parameter estimates when measurement error is ignored. While the Ornstein-Uhlenbeck State Space Model (OUSSM) addresses this in univariate settings, multidimensional extensions…

Applications · Statistics 2026-05-05 Shanglun Li , Toby Kenney , Hong Gu

The purpose of this article is a set-indexed extension of the well-known Ornstein-Uhlenbeck process. The first part is devoted to a stationary definition of the random field and ends up with the proof of a complete characterization by its…

Probability · Mathematics 2013-08-29 Paul Balança , Erick Herbin

We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved…

Statistics Theory · Mathematics 2019-02-25 Yury A. Kutoyants

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

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 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

We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the…

Other Condensed Matter · Physics 2008-12-02 Jaume Masoliver , Josep Perello

I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement…

Instrumentation and Methods for Astrophysics · Physics 2012-10-24 C. A. L. Bailer-Jones

Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval $I$ such that the process starting…

Probability · Mathematics 2020-07-17 Nikita Ratanov

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