Related papers: The OU$^2$ process: Characterising dissipative con…
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 $…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
This paper deals with the realisation of affine constraints on nonreversible stochastic differential equations (SDE) by strong confining forces. We prove that the confined dynamics converges pathwise and on bounded time intervals to the…
In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on $N$ positions. A particle jumps from a position…
We study a model for a massive test particle in a microscopic periodic potential and interacting with a reservoir of light particles. In the regime considered, the fluctuations in the test particle's momentum resulting from collisions…
The system consists of a Brownian particle immersed in a heat bath trapped in optical tweezers with a time-dependent strength acting as an external protocol. In [Phys. Rev. Letts., 98:108301, 2007] the optimal mean work in the overdamped…
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…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the…
We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred location (say, the origin), here we consider…
We study the stochastic growth process in discrete time $x_{i+1} = (1 + \mu_i) x_i$ with growth rate $\mu_i = \rho e^{Z_i - \frac12 var(Z_i)}$ proportional to the exponential of an Ornstein-Uhlenbeck (O-U) process $dZ_t = - \gamma Z_t dt +…
We provide a complete description of the equilibrium fluctuations for diffusive symmetric exclusion processes with long jumps in contact with infinitely extended reservoirs and prove that they behave as generalized Ornstein-Uhlenbeck…
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often…
Thermodynamic uncertainty relations (TURs) delineate tradeoff relations between the thermodynamic cost and the magnitude of an observable's fluctuation. While TURs have been established for various nonequilibrium systems, their…
Tight estimates of exit/containment probabilities are of particular importance in many control problems. Yet, estimating the exit/containment probabilities is non-trivial: even for linear systems (Ornstein-Uhlenbeck processes), the…
Active Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models include also random noise in particle displacement (Wiener process) resulting in a…
In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other…
In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit…
The dynamics of a 2D Bose-Einstein condensate in optical trap is studied taking into consideration fluctuations of the far-off-resonance laser field intensity. The problem is described in the frame of the mean field Gross-Pitaevskii…