Related papers: Quantitative Convergence Rates for Stochastically …

We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L^2 norms. The estimates in total…

We show that the convergence of finite state space Markov chains to stationarity can often be considerably speeded up by alternating every step of the chain with a deterministic move. Under fairly general conditions, we show that not only…

This paper gathers together different conditions which are all equivalent to geometric ergodicity of time-homogeneous Markov chains on general state spaces. A total of 34 different conditions are presented (27 for general chains plus 7 just…

We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties…

In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…

In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…

The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in…

This paper provides sufficient conditions over the sequence of samples and parameters of an adaptive Markov Chain Monte Carlo (MCMC) algorithm to ensure ergodicity with respect to a target distribution that can have unbounded support. These…

The quantitative long time behavior of absorbing, finite, irreducible Markov processes is considered. Via Doob transforms, it is shown that only the knowledge of the ratio of the values of the underlying first Dirichlet eigenvector is…

We introduce an statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail $\sigma$-algebra, short-range…

We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…

We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge…

We apply the method of differential inequalities for the computation of upper bounds for the rate of convergence to the limiting regime for one specific class of (in)homogeneous continuous-time Markov chains. To obtain these estimates, we…

We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…

We investigate the mixing properties of a finite Markov chain in random environment defined as a mixture of a deterministic chain and a chain whose state space has been permuted uniformly at random. This work is the counterpart of a…

We establish the existence and uniqueness of quasi-stationary and quasi-ergodic measures for almost surely absorbed discrete-time Markov chains under weak conditions. We obtain our results by exploiting Banach lattice properties of…

We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system…

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…

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 consider the piecewise-deterministic Markov process obtained by randomly switching between the flows generated by a finite set of smooth vector fields on a compact set. We obtain H\"ormander-type conditions on the vector fields…