Related papers: Exponential ergodicity and steady-state approximat…
This paper is a continuation of the study on the stability speed for Markov processes. It extends the previous study of the ergodic convergence speed to the non-ergodic one, in which the processes are even allowed to be explosive or having…
This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
The explicit criteria for several types of ergodicity of one-dimensional diffusions or birth-death processes have been found out recently in a surprisingly short period. One of the criteria is for exponential ergodicity of birth-death…
We study ergodic properties of Markovian multiclass many-server queues which are uniform over scheduling policies, as well as the size n of the system. The system is heavily loaded in the Halfin-Whitt regime, and the scheduling policies are…
We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second…
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…
We study the infinite-horizon average (ergodic) risk sensitive control problem for diffusion processes under a general structural hypothesis: there is a partition of state space into two subsets, where the controlled diffusion process…
We consider Markov processes that alternate continuous motions and jumps in a general locally compact polish space. Starting from a mechanistic construction, a first contribution of this article is to provide conditions on the dynamics so…
Let $Y$ be an Ornstein-Uhlenbeck diffusion governed by an ergodic finite state Markov process $X$: $dY_t=-\lambda(X_t)Y_tdt+\sigma(X_t)dB_t$, $Y_0$ given. Under ergodicity condition, we get quantitative estimates for the long time behavior…
This work studies the averaging principle for a fully coupled two time-scale system, whose slow process is a diffusion process and fast process is a purely jumping process on an infinitely countable state space. The ergodicity of the fast…
We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…
This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms…
We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…
We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…
We investigate some asymptotic properties of general Markov processes conditioned not to be absorbed by moving boundaries. We first give general criteria involving an exponential convergence towards the Q-process, that is the law of the…