相关论文: About quasi-renewal processes and quasi-regenerati…

We are interested in quasi-stationarity and quasi-ergodicity when the absorbing boundary is moving. First we show that, in the moving boundary case, the quasi-stationary distribution and the quasi-limiting distribution are not well-defined…

In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time…

We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…

Obtaining estimates of the convergence rate of the regenerating process $Q(t)$ whose value at time $t$ is equal to the number of claims in the system $ M \backslash G \backslash \infty $ at this moment, to the limit (stationary) regime.

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

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…

We give a scheme of using the coupling method to obtain strong bounds for the convergence rate of the distribution of the backward renewal process in the total variation distance. This scheme can be applied to a wide class of regenerative…

The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in [Viguerie et al, Appl. Math.…

The adaptive quasi-likelihood analysis is developed for a degenerate diffusion process. Asymptotic normality and moment convergence are proved for the quasi-maximum likelihood estimators and quasi-Bayesian estimators, in the adaptive…

Some characterizations of mixed renewal processes in terms of exchangeability and of different types of disintegrations are given. As a consequence, an existence result for mixed renewal processes, providing also a new construction for…

This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…

Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for…

We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and…

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…

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…

Ageing phenomena are observed in a large variety of dynamical systems exhibiting a slow relaxation from a non-equilibrium initial state. Ageing can be characterised in terms of the linear response R(t,s) at time t to a local perturbation at…

We consider almost upper semi-continuous processes defined on a finite Markov chain. The distributions of the functionals associated with the exit from a finite interval are studied. We also consider some modification of these processes.

We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…

The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and Y. B. Band, J. Phys. B {\bf 32}, 1845 (1999)] is used here to evaluate transition amplitudes for the problem of curve crossing in linear potential grids…