Skip-free Markov chains

DOI10.1090/tran/7773zbMath1481.60137arXiv1903.00139OpenAlexW3104154334MaRDI QIDQ4633780

Pierre Patie, Michael C. H. Choi

Publication date: 6 May 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00139

zbMATH Keywords

cutoffrate of convergenceMarkov chainspotential theoryMartin boundaryspectral theoryfluctuation theorynon-self-adjoint operator

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Probabilistic potential theory (60J45) Boundary theory for Markov processes (60J50)

Related Items (11)

Some harmonic functions for killed Markov branching processes with immigration and culling ⋮ Weak similarity orbit of (log)‐self‐similar Markov semigroups on the Euclidean space ⋮ A spectral theoretical approach for hypocoercivity applied to some degenerate hypoelliptic, and non-local operators ⋮ Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis ⋮ Cutpoints of (1,2) and (2,1) random walks on the lattice of positive half line ⋮ On fluctuation theory for spectrally negative Lévy processes with Parisian reflection below, and applications ⋮ First passage problems for upwards skip-free random walks via the scale functions paradigm ⋮ Metropolis-Hastings reversiblizations of non-reversible Markov chains ⋮ On a gateway between continuous and discrete Bessel and Laguerre processes ⋮ Analysis of non-reversible Markov chains via similarity orbits ⋮ Exit problems for positive self-similar Markov processes with one-sided jumps

Cites Work

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• Strong stationary times via a new form of duality
• Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process
• Denumerable Markov chains. Generating functions, boundary theory, random walks on trees.
• On hitting times and fastest strong stationary times for skip-free and more general chains
• Total variation cutoff in birth-and-death chains
• Separation cut-offs for birth and death chains
• The cutoff phenomenon for ergodic Markov processes
• Continuous-time Markov chains. An applications-oriented approach
• The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes
• M. G. Krein's lectures on entire operators
• Geometric ergodicity and hybrid Markov chains
• Cauchy problem of the non-self-adjoint Gauss-Laguerre semigroups and uniform bounds for generalized Laguerre polynomials
• Purely excessive functions and hitting times of continuous-time branching processes
• On a gateway between continuous and discrete Bessel and Laguerre processes
• Computing cutoff times of birth and death chains
• A Random Walk with a Skip-Free Component and the Lagrange Inversion Formula
• Separation cutoff for upward skip-free chains
• On absorption times and Dirichlet eigenvalues
• A Combinatorial Lemma and Its Application to Probability Theory
• Denumerable Markov Processes (II)
• The Differential Equations of Birth-and-Death Processes, and the Stieltjes Moment Problem
• Spectral Theory for Skip-Free Markov Chains
• Hypocoercivity
• Shuffling Cards and Stopping Times
• Fluctuation identities for lévy processes and splitting at the maximum
• An eigenvalue decomposition for first hitting times in random walks
• Birth, immigration and catastrophe processes
• Singular Values, Diagonal Elements, and Convexity
• Applied Probability and Queues
• Infinitely Divisible Distributions and Bessel Functions Associated with Random Walks
• BOUNDARY THEORY OF MARKOV PROCESSES (THE DISCRETE CASE)
• Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes
• Markov Processes, Brownian Motion, and Time Symmetry
• Diffusion Processes in One Dimension
• Spectral theory for the differential equations of simple birth and death processes

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