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On the conditional covariance condition in the martingale CLT

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Abstract

The paper develops a method allowing one to figure out how a convergence rate in the martingale central limit theorem depends on the conditional covariance structure of the martingale. The method is based on constructing “stopping projections” that control the behavior of the conditional covariances of martingale differences. A discrete time martingale taking values in either finite or infinite dimensional Hilbert space is considered.

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Authors
  1. A. Račkauskas
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Additional information

Research supported by the International Science Foundation grant LI000.

Vilnius University, Naugarduko 24, 2006, Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 1, pp. 118–131, January—March, 1995.

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Račkauskas, A. On the conditional covariance condition in the martingale CLT. Lith Math J 35, 93–104 (1995). https://doi.org/10.1007/BF02337759

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  • DOI: https://doi.org/10.1007/BF02337759

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