Related papers: Small time asymptotics in local limit theorems for…

We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…

The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…

We consider a Markov chain $\{X_n\}_{n=0}^\8$ on $\R^d$ defined by the stochastic recursion $X_{n}=M_n X_{n-1}+Q_n$, where $(Q_n,M_n)$ are i.i.d. random variables taking values in the affine group $H=\R^d\rtimes {\rm GL}(\R^d)$. Assume that…

We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish…

Based on discrete observations $X_0,X_{\Delta},\dots, X_{n\Delta}$ for $\Delta=n^{-\gamma}$ with $\gamma\in [0,1)$ of the null-recurrent dynamic $dX_t = \sigma(X_t)dW_t$ with a Brownian motion $W$ and $\sigma(x)=\alpha\mathbb{1}\{x<\rho\} +…

We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…

Let $(X_t)$ be a discrete time Markov chain on a general state space. It is well-known that if $(X_t)$ is aperiodic and satisfies a drift and minorization condition, then it converges to its stationary distribution $\pi$ at an exponential…

For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary…

We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…

We study a class of high-frequency path functionals for diffusions with singular thresholds or boundaries, where the process exhibits either (i) skweness, oscillating coefficients, and stickiness, or (ii) sticky reflection. The functionals…

We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…

We study time-inhomogeneous Markov chains to obtain quantitative results on their asymptotic behavior. We use Poincar\'e, Nash, and logarithmic-Sobolev inequalities. We assume that our Markov chain admits a finite invariant measure at each…

We consider the asymptotics of the invariant measure for the process of the empirical spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.…

We consider a form of state-dependent drift condition for a general Markov chain, whereby the chain subsampled at some deterministic time satisfies a geometric Foster-Lyapunov condition. We present sufficient criteria for such a drift…

This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…

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 $t\to\infty$.…

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…

We study a one-dimensional diffusion $X$ in a drifted Brownian potential $W\_\kappa$, with $ 0\textless{}\kappa\textless{}1$, and focus on the behavior of the local times $(\mathcal{L}(t,x),x)$ of $X$ before time $t\textgreater{}0$.In…

There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were…