Related papers: Coupling Markov chains with a common image chain

We consider a stationary regularly varying time series which can be expressedas a function of a geometrically ergodic Markov chain. We obtain practical conditionsfor the weak convergence of the tail array sums and feasible estimators…

Dependence coefficients have been widely studied for Markov processes defined by a set of transition probabilities and an initial distribution. This work clarifies some aspects of the theory of dependence structure of Markov chains…

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…

We consider a time-homogeneous Markov chain $X_n$, $n\ge0$, valued in ${\bf R}$. Suppose that this chain is transient, that is, $X_n$ generates a $\sigma$-finite renewal measure. We prove the key renewal theorem under condition that this…

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…

We consider the recurrence and transience problem for a time-homogeneous Markov chain on the real line with transition kernel $p(x,\mathrm{d}y)=f_x(y-x)\,\mathrm{d}y$, where the density functions $f_x(y)$, for large $|y|$, have a power-law…

Let $Q$ be a probability measure on a finite group $G$, and let $H$ be a subgroup of $G$. We show that a necessary and sufficient condition for the random walk driven by $Q$ on $G$ to induce a Markov chain on the double coset space…

We construct different classes of lumpings for a family of Markov chain products which reflect the structure of a given finite poset. We use essentially combinatorial methods. We prove that, for such a product, every lumping can be obtained…

In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niew\k{e}g\l owski (2015). Here, we turn our attention to the study of Markov consistency and…

We establish that if a sequence of electrical networks equipped with conductance measures converges in the local Gromov--Hausdorff-vague topology and satisfies certain non-explosion and metric-entropy conditions,then the sequence of…

We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics which do not satisfy the mixing…

The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all…

A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the…

For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular,…

We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…

Let $X_1,X_2,\ldots$ and $Y_1,Y_2,\ldots$ be two random sequences so that every random variable takes values in a finite set $\mathbb{A}$. We consider a global similarity score $L_n:=L(X_1,\ldots,X_n;Y_1,\ldots,Y_n)$ that measures the…

We give recurrence and transience criteria for two cases of time-homogeneous Markov chains on the real line with transition kernel $p(x,dy)=f_x(y-x)dy$, where $f_x(y)$ are probability densities of symmetric distributions and, for large…

We initiate the study of mixing times of Markov chain under monotone censoring. Suppose we have some Markov Chain $M$ on a state space $\Omega$ with stationary distribution $\pi$ and a monotone set $A \subset \Omega$. We consider the chain…

We provide a nonasymptotic analysis of convergence to stationarity for a collection of Markov chains on multivariate state spaces, from arbitrary starting points, thereby generalizing results in [Khare and Zhou Ann. Appl. Probab. 19 (2009)…

Let $(X_n)_{n \ge 0}$ be an irreducible, aperiodic, homogeneous Markov chain, with state space a totally ordered finite alphabet of size $m$. Using combinatorial constructions and weak invariance principles, we obtain the limiting shape of…