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On the maximal inequalities of Burkholder, Davis and Gundy. (English) Zbl 1335.60064
Summary: We give a proof of the maximal inequalities of Burkholder, Davis and Gundy for real as well as Hilbert-space-valued local martingales using almost only stochastic calculus. Some parts, especially in the infinite dimensional case, appear to be original.

60G44 Martingales with continuous parameter
60H05 Stochastic integrals
60G07 General theory of stochastic processes
46N30 Applications of functional analysis in probability theory and statistics
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