Related papers: Total variation approximation for quasi-equilibriu…
In a first part, we prove a Lyapunov-type criterion for the $\xi\_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second…
In the present work we characterize the existence of quasistationary distributions for diffusions on $(0,\infty)$ allowing singular behavior at $0$ and $\infty$. If absorption at 0 is certain, we show that there exists a quasistationary…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
"Quasi-stationary" states are approximately time-independent out of equilibrium states which have been observed in a variety of systems of particles interacting by long-range interactions. We investigate here the conditions of their…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we…
We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…
We characterise all the quasi-stationary distributions and the Q-process associated with a continuous state branching process that explodes in finite time. We also provide a rescaling for the continuous state branching process conditioned…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…