Some New Maximal Inequalities
Peter Harremoes
Statistics and Probability Letters 2007.

## Abstract

New maximal inequalities for non-negative martingales are proved. The inequalities are tight and strengthen well-known maximal inequalities by Doob. The inequalities relates martingales to information divergence and imply convergence of $X\ln X$ bounded martingales. Similar results holds for stationary sequences

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EPrint Type: Article Project Keyword UNSPECIFIED Learning/Statistics & Optimisation 3466 Peter Harremoes 11 February 2008