Related papers: Diffusions conditioned on occupation measures
Large dynamical fluctuations - atypical realizations of the dynamics sustained over long periods of time - can play a fundamental role in determining the properties of collective behavior of both classical and quantum non-equilibrium…
We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they…
In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
In this paper we study the moment generating function and the moments of occupation time functionals of one-dimensional diffusions. Assuming, specifically, that the process lives on $\mathbb{R}$ and starts at~0, we apply Kac's moment…
We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The…
In order to study the stochastic Markov processes conditioned on a specific value of a time-integrated observable, the concept of ensembles of trajectories has been recently used extensively. In this paper, we consider a generic…
As a main example for the superstatistics approach, we study a Brownian particle moving in a d-dimensional inhomogeneous environment with macroscopic temperature fluctuations. We discuss the average occupation time of the particle in…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
We revisit the work of Dhar and Majumdar [Phys. Rev. E 59, 6413 (1999)] on the limiting distribution of the temporal mean $M_{t}=t^{-1}\int_{0}^{t}du \sign y_{u}$, for a Gaussian Markovian process $y_{t}$ depending on a parameter $\alpha $,…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (2006) in the field of Single Molecule FRET spectroscopy. There, a single molecule fluctuates between two or more states,…
Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the…