Multidimensional renewal theory in the non-centered case: application to strongly ergodic Markov chains

DOI10.1007/s11118-012-9282-0zbMath1273.60083arXiv1110.3603OpenAlexW1986599579MaRDI QIDQ1935439

Denis Guibourg, Loïc Hervé

Publication date: 15 February 2013

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3603

zbMATH Keywords

Fourier techniquesMarkov random walksmultidimensional renewal theory

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Renewal theory (60K05)

Related Items (2)

Local limit theorem for a Markov additive process on with a null recurrent internal Markov chain ⋮ Renewal theory for transient Markov chains with asymptotically zero drift

Cites Work

• A uniform Berry-Esseen theorem on \(M\)-estimators for geometrically ergodic Markov chains
• Limit theorems for stationary Markov processes with \(L^{2}\)-spectral gap
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• Markov chains and stochastic stability
• Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
• Théorie du renouvellement pour des chaînes semi-markoviennes transientes. (Renewal theory for transient semi-Markov chains)
• Renewal theorem for strongly ergodic Markov chains : application to Lipschitz iterative models
• Asymptotic estimates of the Green functions and transition probabilities for Markov additive processes
• Asymptotic expansions in multidimensional Markov renewal theory and first passage times for Markov random walks
• The Nagaev-Guivarc’h method via the Keller-Liverani theorem
• Propriétés de mélange du flot des chambres de Weyl des groupes de Ping-Pong
• A Central Limit Theorem for Contractive Stochastic Dynamical Systems
• The Martin Boundary for Random Walk
• An Analogue of the Renewal Theorem in Higher Dimensions
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