A functional central limit theorem for regenerative chains

G. Maillard, S. Schöpfer

Published 2008-01-15, updated 2008-09-24Version 2

Using the regenerative scheme of Comets, Fern\'andez 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.