相关论文: Continuous-time block-monotone Markov chains and t…

Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a key role in reachability analysis…

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 981-1101], Rosenthal…

First, under a geometric ergodicity assumption, we provide some limit theorems and some probability inequalities for the bifurcating Markov chains (BMC). The BMC model was introduced by Guyon to detect cellular aging from cell lineage, and…

We introduce block Markov chains (BMCs) indexed by an infinite rooted tree. It turns out that BMCs define a new class of tree-indexed Markovian processes. We clarify the structure of BMCs in connection with Markov chains (MCs) and Markov…

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…

Clustering algorithms frequently require the number of clusters to be chosen in advance, but it is usually not clear how to do this. To tackle this challenge when clustering within sequential data, we present a method for estimating the…

Variable-length Markov chains on finite quivers provide a natural framework for context-dependent stochastic growth under incidence constraints. I study quiver-valued variable-length Markov chains observed through finite boundary windows…

When the state space of a discrete state space positive recurrent Markov chain is infinite or very large, it becomes necessary to truncate the state space in order to facilitate numerical computation of the stationary distribution. This…

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…

Labeled Markov Chains (or LMCs for short) are useful mathematical objects to model complex probabilistic languages. A central challenge is to compare two LMCs, for example to assess the accuracy of an abstraction or to quantify the effect…

By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identical smaller chains around a directed cycle, are…

The time to converge to the steady state of a finite Markov chain can be greatly reduced by a lifting operation, which creates a new Markov chain on an expanded state space. For a class of quadratic objectives, we show an analogous behavior…

This paper provides full classification of dynamics for continuous time Markov chains (CTMCs) on the non-negative integers with polynomial transition rate functions. Such stochastic processes are abundant in applications, in particular in…

We are interested in quasi-stationarity and quasi-ergodicity when the absorbing boundary is moving. First we show that, in the moving boundary case, the quasi-stationary distribution and the quasi-limiting distribution are not well-defined…

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…

The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…

We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the…

Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…

In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model…