INVARIANCE PRINCIPLES WITH LOGARITHMIC AVERAGING FOR MARTINGALES

Author: F. Chaabane

Source: Studia Scientiarum Mathematicarum Hungarica, Volume 37, Numbers 1-2, 4 December 2001 , pp. 21-52(32)

Publisher: Akademiai Kiado

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Abstract:

For discrete martingales we show that empirical measures related to the central limit theorem when appropriately weighted converge weakly toward a Gaussian measure,for almost all trajectories.Thi result enables u to derive a weighted trong law of the large number for which we pecify both weak and trong rate of convergence.

Document Type: Research article

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