A functional central limit theorem for regenerative chains

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.

14 pages

References in corpus (1)

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