Related papers: Occupation times via Bessel functions
The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are…
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…
We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we…
In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not…
We study the time evolution of occupation numbers for interacting Fermi-particles in the situation when exact compound states are "chaotic". This situation is generic for highly excited many-particles states in heavy nuclei, complex atoms,…
Molecular simulations as well as single molecule experiments have been widely analyzed in terms order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive,…
In this paper excursions of a stationary diffusion in stationary state are studied. In particular, we compute the joint distribution of the occupation times $I^{(+)}_t$ and $I^{(-)}_t$ above and below, respectively, the observed level at…
We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model, the total occupation measure is known to…
Smoothness and asymptotic behaviors are studied for the densities of the law of the occupation time on the positive line for Bessel bridges and the normalized excursion of strictly stable processes. The key role is played by these…
With respect to a class of long-range exclusion processes on $\mathbb{Z}^d$, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the…
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…
We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function W. The approach does not require sharp bounds…
We study the limit fluctuations of the rescaled occupation time process of a branching particle system in $\mathbb{R}^d$, where the particles are subject to symmetric $\alpha$-stable migration ($0<\alpha\leq2$), critical binary branching,…
We study the empirical process arising from a multi-dimensional diffusion process with periodic drift and diffusivity. The smoothing properties of the generator of the diffusion are exploited to prove the Donsker property for certain…
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…
A stochastic process $X$ becomes occupied when it is enlarged with its occupation flow $\mathcal{O}$ that tracks the time spent by the path at each level. When $X$ is Markov, the occupied process $(\mathcal{O},X)$ enjoys a Markov structure…
We introduce two natural notions for the occupation measure of a function $V$ with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…