Related papers: The OU$^2$ process: Characterising dissipative con…
Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a…
Noise aids the encoding of continuous signals into pulse sequences by way of stochastic resonance and endows the encoding device with a preferred frequency. We study encoding by a threshold device based on the Ornstein-Uhlenbeck process,…
In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows. The fluctuating pressure forces acting on a fluid particle are taken to be a colored…
Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to L\'evy-driven…
We study the density fluctuations at equilibrium of the multi-species stirring process, a natural multi-type generalization of the symmetric (partial) exclusion process. In the diffusive scaling limit, the resulting process is a system of…
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,…
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…
The Ornstein--Uhlenbeck Particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time-scale. Here we investigate the influence of external potentials on an ideal suspension…
Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to…
We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function…
Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to…
We consider passive Brownian particles trapped in an "imperfect" harmonic trap. The trap is imperfect because it is randomly turned off and on, and as a result, particles fail to equilibrate. Another way to think about this is to say that a…
We investigate the distributional properties of two generalized Ornstein-Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively. The said distributions turn out to be related to…
The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive L\'evy drivers - understood as abrupt thermalization of the…
We have developed a new in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are…
First-passage time (FPT) of an Ornstein-Uhlenbeck (OU) process is of immense interest in a variety of contexts. This paper considers an OU process with two boundaries, one of which is absorbing while the other one could be either reflecting…
We consider equations of nonlinear transport on the circle with regular self interactions appearing in aggregation models and deterministic mean field dynamics. We introduce a random perturbation of such systems through a stochastic…
To investigate the complex dynamics of a biological neuron that is subject to small random perturbations we can use stochastic neuron models. While many techniques have already been developed to study properties of such models, especially…
We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two…
The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a…