Related papers: The Algebra of Reversible Markov Chains

The growing attention on cryptocurrencies has led to increasing research on digital stock markets. Approaches and tools usually applied to characterize standard stocks have been applied to the digital ones. Among these tools is the…

Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…

The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov…

We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…

In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this…

For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\"obius monotonicity of the chain. We show relations of M\"obius monotonicity to other definitions of monotone chains.…

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 provide explicit expressions for the constants involved in the characterisation of ergodicity of sub-geometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation…

We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic…

We define the spectral gap of a Markov chain on a finite state space as the second-smallest singular value of the generator of the chain, generalizing the usual definition of spectral gap for reversible chains. We then define the relaxation…

Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…

In a general setting we solve the following inverse problem: Given a positive operators $R$, acting on measurable functions on a fixed measure space $(X,\mathcal B_X)$, we construct an associated Markov chain. Specifically, starting with a…

We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…

Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via Markov chain Monte Carlo method. In this paper we derive explicit forms of Markov bases for change point…

Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…

In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…

Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a reversible Markov chain can improve its connectivity while…