Another view on martingale central limit theorems

Peter Gaenssler and Konrad Joos

Stochastic Processes and their Applications, 1992, vol. 40, issue 2, 181-197

Abstract: Based on the martingale version of the Skorokhod embedding Heyde and Brown (1970) established a bound on the rate of convergence in the central limit theorem (CLT) for discrete time martingales having finite moments of order 2+2[delta] with 0 0 was proved in Haeusler (1988). This paper presents a rather quick access based solely on truncation, optional stopping, and prolongation techniques for martingale difference arrays to obtain other upper bounds for sup ([phi]being the standard normal d.f.) yielding weak sufficient conditions for the asymptotic normality of . It is shown that our approach also yields two types of martingale central limit theorems with random norming.

Keywords: CLT's; for; martingales; Lindeberg-Lévy; method; rates; of; convergence; sufficient; conditions; for; asymptotic; normality; CLT's; with; random; norming (search for similar items in EconPapers)
Date: 1992
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