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Related papers: Markov chains revisited

200 papers

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…

Statistics Theory · Mathematics 2016-10-06 Lionel Truquet

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…

Machine Learning · Computer Science 2023-06-01 Patrick Seifner , Ramses J. Sanchez

We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…

Probability · Mathematics 2012-10-11 Fangjun Xu

. Markov chains in time, such as simple random walks, are at the heart of probability. In space, due to the absence of an obvious definition of past and future, a range of definitions of Markovianity have been proposed. In this paper, after…

Probability · Mathematics 2007-06-13 M. N. M. van Lieshout

In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a…

Probability · Mathematics 2017-11-09 Michel Benaïm , Florian Bouguet , Bertrand Cloez

The main goal of this text is comprehensive study of time homogeneous Markov chains on the real line whose drift tends to zero at infinity, we call such processes Markov chains with asymptotically zero drift. Traditionally this topic is…

Probability · Mathematics 2023-09-06 Denis Denisov , Dmitry Korshunov , Vitali Wachtel

The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is…

Probability · Mathematics 2014-02-06 Yinshan Chang , Yves Le Jan

The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the…

Probability · Mathematics 2016-04-07 Ioannis Papastathopoulos , Kirstin Strokorb , Jonathan A. Tawn , Adam Butler

Markov Chains offer ideal conditions for the study and mathematical modelling of a certain kind of situations depending on random variables. The basic concepts of the corresponding theory were introduced by Markov in 1907 on coding literary…

Optimization and Control · Mathematics 2016-01-09 Michael Gr. Voskoglou

Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…

Computation · Statistics 2013-10-21 Vinayak Rao , Yee Whye Teh

Potential theory has important applications in various fields such as physics, finance, and biology. In this paper, we investigate the potentials of two classic types of discrete-time skip-free Markov chains: upward skip-free and downward…

Probability · Mathematics 2025-02-04 Wendi Li , Jinpeng Liu , Yuanyuan Liu

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…

Computation · Statistics 2017-08-30 James E. Johndrow , Jonathan C. Mattingly , Sayan Mukherjee , David Dunson

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

Optimization and Control · Mathematics 2016-09-20 Damjan Škulj

This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…

Probability · Mathematics 2019-07-02 Roy Cerqueti , Emilio De Santis

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

Social and Information Networks · Computer Science 2012-11-01 J. Ray , A. Pinar , C. Seshadhri

Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…

Probability · Mathematics 2017-02-01 Tingyue Gan , Maria Cameron

We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…

Statistics Theory · Mathematics 2015-02-02 Christophe Andrieu , Vladislav B. Tadić , Matti Vihola

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…

Disordered Systems and Neural Networks · Physics 2012-03-12 E. S. Roberts , A. Annibale , A. C. C. Coolen

It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…

Probability · Mathematics 2015-03-17 Steven N. Evans , Rudolf Gruebel , Anton Wakolbinger

This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…

Probability · Mathematics 2010-10-18 Stéphane Attal