A functional central limit theorem for regenerative chains

2008/01/15 by G. Maillard, Maillard, G., Samuel Schöpfer +2
Mathematics · #37A05 #60F05 #60G10 (Primary) #60K05 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and statistical mechanics #math.PR #msc:37A05 #msc:60F05 #msc:60G10 #msc:60K05

paper · pdf · doi:10.48550/arxiv.0801.2263

14 pages

openalex publication_date 2008/01/15 · arxiv created 2008/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the regenerative scheme of Comets, Fernández and Ferrari (2002), we establish a functional central limit theorem (FCLT) for discrete time stochastic processes (chains) with summable memory decay. Furthermore, under stronger assumptions on the memory decay, we identify the limiting variance in terms of the process only. As applications, we define classes of binary autoregressive processes and power-law Ising chains for which the FCLT is fulfilled.

Citations

• Fluctuations of the Empirical Entropies of a Chain of Infinite Order

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