We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments of martingales. Several statistical applications to autoregressive and branching processes are also provided.
and Csáki, E.
, A universal result in almost sure central limit theory,
Stochastic Process. Appl.94
Csáki E., 'A universal result in almost sure central limit theory' (2001) 94Stochastic Process. Appl.: 105-134.
Csáki E.A universal result in almost sure central limit theoryStochastic Process. Appl.200194105134)| false
, Almost sure limit theorem for martingales, in:
Limit Theorems in Probability and Statistics II
(I. Berkes, E. Csáki, M. Csörgő, eds.) J. Bolyai Mathematical Society, Budapest (2002), 367–390.
Lifshits M., '', in Limit Theorems in Probability and Statistics II, (2002) -.
Lifshits M.Limit Theorems in Probability and Statistics II2002)| false
, Lecture notes on almost sure limit theorems,
(2001), Lille, 1–25.
Lifshits M., 'Lecture notes on almost sure limit theorems' (2001) 54Publications IRMA: 1-25.
Lifshits M.Lecture notes on almost sure limit theoremsPublications IRMA200154125)| false