Related papers: Probability and moment inequalities for additive f…
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…
We consider an additive functional driven by a time-inhomogeneous Markov chain with a finite state space. Our study focuses on the joint distribution of the two-sided exit time and the state of the driving Markov chain at the time of exit,…
We prove a version of McDiarmid's bounded differences inequality for Markov chains, with constants proportional to the mixing time of the chain. We also show variance bounds and Bernstein-type inequalities for empirical averages of Markov…
Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a…
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased…
For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of…
It is known that the Dobrushin's ergodicity coefficient is one of the effective tools to study a behavior of non-homogeneous Markov chains. In the present paper, we define such an ergodicity coefficient of a positive mapping defined on…
We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities.…
Let $(\xi_n)_{n=0}^\infty$ be a nonhomogeneous Markov chain taking values from finite state-space of $\mathbf{X}=\{1,2,\ldots,b\}$. In this paper, we will study the generalized entropy ergodic theorem with almost-everywhere and…
We study properties of the Laplace transforms of non-negative additive functionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [18] to study bifurcating processes with ancestral dependence. We…
An important step in the Markov reward approach to error bounds on stationary performance measures of Markov chains is to bound the bias terms. Affine functions have been successfully used for these bounds for various models, but there are…
We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…
In our earlier paper, a generalized Dobrushin ergodicity coefficient of Markov operators (acting on abstract state spaces) with respect to a projection $P$, has been introduced and studied. It turned out that the introduced coefficient was…
We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…
We prove explicit error bounds for Markov chain Monte Carlo (MCMC) methods to compute expectations of functions with unbounded stationary variance. We assume that there is a $p\in(1,2)$ so that the functions have finite $L_p$-norm. For…
This paper is interested in proving correlation inequalities of the FKG-type for various stochastic processes in continuous time. The pivotal tool which yields these correlation inequalities is an approximation with (possibly conditioned)…
We study Poisson's equation in the context of general state space Markov chains. For chains satisfying a contraction assumption w.r.t. a Wasserstein distance, we show that a solution exists for Lipschitz functions and investigate its…
A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized)…
In this short note we provide an elementary proof that a certain type of nonuniform sequential Doeblin minorization condition implies non-uniform sequential "geometric" ergodicity. Using this result several limit theorems for inhomogeneous…