Related papers: Substitution Markov chains and Martin boundaries
Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the…
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 present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of N sites. It is partially asymmetric…
For a relatively large class of well-behaved absorbing (or killed) finite Markov chains, we give detailed quantitative estimates regarding the behavior of the chain before it is absorbed (or killed). Typical examples are random walks on…
We presented in \cite{bl2,bl7} an approach to derive the metastable behavior of continuous-time Markov chains. We assumed in these articles that the Markov chains visit points in the time scale in which it jumps among the metastable sets.…
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large…
In this note, a general approach to the study of non-stationary Markov chains with catastrophes and the corresponding queuing models is considered, as well as to obtain estimates of the limiting regime itself. As an illustration, an example…
This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a…
In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…
Markov chain models are used in various fields, such behavioral sciences or econometrics. Although the goodness of fit of the model is usually assessed by large sample approximation, it is desirable to use conditional tests if the sample…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
We study the discrete-time evolution of a transformation on a set of probability measures that is up-dated combining independently the marginals on the atoms of partitions. This model was recently introduced in Baake, Baake and Salamat…
We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through…