Related papers: Measure Concentration of Markov Tree Processes
The filtering problem for finite state Markov chains is revisited, when the intensity of the observation noise increases. We give a description of conditional measure concentration around the invariant distribution of the signal and derive…
In this paper we show an alternative approach to the concentration of truncated variation for stochastic processes on a real line. Our method is based on the moments control and can be used to generalize the results to the case of processes…
Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed…
We develop a Markov process viewpoint for discrete circular distributions motivated by directional-statistics settings where angles are observed on a finite grid and evolve over time. On the $m$-point discrete circle, the cycle graph, we…
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…
We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains.…
We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general…
In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We…
The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…
The problem of efficiently sampling from a set of (undirected, or directed) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the…
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…
We prove that moderate deviations for empirical measures for countable nonhomogeneous Markov chains hold under the assumption of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chains in Ces\`aro…
The main purpose of this work is to study self-similar branching Markov chains. First we will construct such a process. Then we will establish certain Limit Theorems using the theory of self-similar Markov processes.