Related papers: Comparison inequalities and fastest-mixing Markov …

We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…

We study the relationship between functional inequalities for a Markov kernel on a metric space $X$ and inequalities of transportation distances on the space of probability measures $\mathcal{P}(X)$. Extending results of Luise and Savar\'e…

We study perturbation theory and uniform ergodicity for discrete-time Markov chains on general state spaces in terms of the uniform moments of the first hitting times on some set. The methods we adopt are different from previous ones. For…

We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…

Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a…

Sampling from the conditional (or posterior) probability distribution of the latent states of a Hidden Markov Model, given the realization of the observed process, is a non-trivial problem in the context of Markov Chain Monte Carlo. To do…

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…

We develop kernel criteria for the likelihood-ratio, hazard-rate, usual stochastic, and relative log-concavity orders in parametric families of univariate probability laws with densities. The score is the derivative of the log density with…

We derive explicit upper bounds for the $\bar{d}$-distance between a chain of infinite order and its canonical $k$-steps Markov approximation. Our proof is entirely constructive and involves a "coupling from the past" argument. The new…

We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary…

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…

We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…

Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. This paper provides explicit connections between the $V$-geometric ergodicity of $P$ and that of finite-rank nonnegative sub-Markov kernels $\Pc_k$…

Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…

We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…

We study two types of Metropolis-Hastings (MH) reversiblizations for non-reversible Markov chains with Markov kernel $P$. While the first type is the classical Metropolised version of $P$, we introduce a new self-adjoint kernel which…

The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. In 1996, Diaconis surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite…

In this paper, we consider chains of infinite order on countable state spaces with prohibited transitions. We give a set of sufficient conditions on the structure of the probability kernels of the chains to have at most one stationary…

A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…