A functional central limit theorem for regenerative chains

Details A functional central limit theorem for regenerative chains A functional central limit theorem for regenerative chains

2008-01-15

arxiv.org/abs/0801.2263v2

Mathematics

Probability

14 pages

Scientific paper

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.

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