Related papers: Substitution Markov chains and Martin boundaries
Advanced observational facilities allow to trace back the chemical evolution of the Universe, on the one hand, from local objects of different ages and, secondly, by direct observations of redshifted objects. The chemical enrichment serves…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
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…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…
Markov chains have long been used for generating random variates from spatial point processes. Broadly speaking, these chains fall into two categories: Metropolis-Hastings type chains running in discrete time and spatial birth-death chains…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
Isoperimetric inequalities form a very intuitive yet powerful characterization of the connectedness of a state space, that has proven successful in obtaining convergence bounds. Since the seventies they form an essential tool in…
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive…
The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
Nonlinear Markov chains with finite state space have been introduced in Kolokoltsov (2010). The characteristic property of these processes is that the transition probabilities do not only depend on the state, but also on the distribution of…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…
Consider an irreducible Markov chain which satisfies a ratio limit theorem, and let $\rho$ be the spectral radius of the chain. We investigate the relation of the the $\rho\,$-Martin boundary with the boundary induced by the…
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…