Related papers: Residence Time Statistics for Normal and Fractiona…
We provide a statistical framework for characterizing stochastic particle production in the early universe via a precise correspondence to current conduction in wires with impurities. Our approach is particularly useful when the…
We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than…
We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias…
We consider the influence of active speed fluctuations on the dynamics of a $d$-dimensional active Brownian particle performing a persistent stochastic motion. We use the Laplace transform of the Fokker-Planck equation to obtain exact…
Equation of long-range particle drift and diffusion on three-dimensional physical lattice is suggested. This equation can be considered as a lattice analogof space-fractional Fokker-Planck equation for continuum. The lattice approach gives…
We study ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin/fat tailed distributions, the normalized/non-normalised invariant…
We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form…
Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and L\'evy processes. By contrast, two-time occupation statistics, which…
We study the effects of an intermittent harmonic potential of strength $\mu = \mu_0 \nu$ -- that switches on and off stochastically at a constant rate $\gamma$, on an overdamped Brownian particle with damping coefficient $\nu$. This can be…
Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for…
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…
We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…
Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For…
During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…
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…
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 2003) calculated the mean first exit time of a domain of a particle undergoing a randomly reoriented ballistic motion which starts from the boundary. They showed…
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…
Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the…
We study here the escape time for the fastest diffusing particle from the boundary of an interval with point-sink killing sources. Killing represents a degradation that leads to the probabilistic removal of the moving Brownian particles. We…
We discuss physical and mathematical aspects of the over-damped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are…