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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.

MSC:

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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