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Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
Large vacuum fluctuations of a quantum stress tensor operator can be described by the asymptotic behavior of the probability distribution of the time or spacetime averaged operator. Here we focus on the case of stress tensor operators…
In this paper, we study the asymptotic behavior of the number of crossings by a one-dimensional diffusion of a threshold where the process exhibits stickiness. We distinguish three types of crossings and show that to each type corresponds a…
We consider the Markov random flight $\bold X(t), \; t>0,$ in the three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$ and the uniform choice of the initial and each new direction at random time instants that form a…
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…
We study a two state ``jumping diffusivity'' model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$, with random waiting times in both states whose distribution is rather general. In the limit of…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
A method-of-moments scheme is invoked to compute the asymptotic, long-time mean (or composite) velocity and dispersivity (effective diffusivity) of a two-state particle undergoing one-dimensional convective-diffusive motion accompanied by a…
We study properties of a piecewise deterministic Markov process modeling the changes in concentration of specific antibodies. The evolution of densities of the process is described by a stochastic semigroup. The long-time behaviour of this…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density…
By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in…
The goal of this paper is to propose a new approach to asymptotic analysis of the finite predictor for stationary sequences. It produces the exact asymptotics of the relative prediction error and the partial correlation coefficients. The…
A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not…
We extend the concept of Lyapunov 1-forms for the case of diffu- sion processes to study its asymptotic behavior. We give some examples and a condition for the existence of these objects.
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point is assumed unknown (nonrandom). The topic of interest is…