Limit theorems for stationary Markov processes with \(L^{2}\)-spectral gap

DOI10.1214/11-AIHP413zbMath1245.60068arXiv1201.4579OpenAlexW2124306784MaRDI QIDQ424699

James Ledoux, Déborah Ferré, Loïc Hervé

Publication date: 4 June 2012

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.4579

zbMATH Keywords

functional central limit theoremcentral limit theorem\(M\)-estimatoradditive functionalEdgeworth expansionlocal limit theoremgeometric ergodicityuniform ergodicityBerry-Esseen theoremMarkov additive process\(\rho\)-mixing Markov chain\(L^2\)-spectral gap propertydiscrete or continuous-time Markov processFourier operatorMarkov random walkstationary Markov process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov processes: estimation; hidden Markov models (62M05) Continuous-time Markov processes on general state spaces (60J25) Discrete-time Markov processes on general state spaces (60J05) Ergodic theorems, spectral theory, Markov operators (37A30) Local time and additive functionals (60J55)

Related Items (11)

Markov random geometric graph, MRGG: a growth model for temporal dynamic networks ⋮ A computable bound of the essential spectral radius of finite range metropolis-Hastings kernels ⋮ Geometric ρ-Mixing Property of the Interarrival Times of a Stationary Markovian Arrival Process ⋮ A local limit theorem for densities of the additive component of a finite Markov additive process ⋮ On the local limit theorems for psi-mixing Markov chains ⋮ Multidimensional renewal theory in the non-centered case: application to strongly ergodic Markov chains ⋮ Functional central limit theorems and \(P(\phi )_1\)-processes for the relativistic and non-relativistic Nelson models ⋮ Local limit theorem for a Markov additive process on with a null recurrent internal Markov chain ⋮ Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains ⋮ On the local limit theorems for lower psi-mixing Markov chains ⋮ Parametric first-order Edgeworth expansion for Markov additive functionals. Application to \(M\)-estimations

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