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VI: 19, 198-201, LNM 258 (1972)
RAO, Murali
Doob's decomposition and Burkholder's inequalities (Martingale theory)
The ``Burkholder inequalities'' referred here are the weak-$L^1$ estimates for the supremum of a martingale transform and for the square function proved by Burkholder (Ann. Math. Stat., 37, 1966) for $L^1$-bounded discrete time martingales. The original proof was quite sophisticated, while here these inequalities are deduced from an estimate on the (elementary) Doob decomposition of a discrete supermartingale
Comment: This little-known paper would probably deserve a modern translation in continuous time
Keywords: Burkholder inequalities, Decomposition of supermartingales
Nature: Original
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