A Functional Central Limit Theorem for Regenerative Chains
2008, v.14, №4, 583-598
Using the regenerative scheme of [F. Comets, R. Fernandez and P. Ferrari, Process with long memory: Regenerative construction and perfect simulation, Ann. Appl. Probab., 2002, v.12, pp.921-943], 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.
Keywords: chains,central limit theorem,regeneration,renewal process