Burkholder's submartingales from a stochastic calculus perspective

Details Burkholder's submartingales from a stochastic calculus perspective Burkholder's submartingales from a stochastic calculus perspective

2007-05-24

arxiv.org/abs/0705.3633v1

Mathematics

Probability

7 pages

Scientific paper

We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in terms of a squared Brownian motion and of some appropriate powers of its maximum. Our techniques involve elementary stochastic calculus, as well as the Doob-Meyer decomposition of continuous submartingales. These results can be used to obtain an explicit expression of the constants appearing in the Burkholder-Davis-Gundy inequalities. A connection with some balayage formulae is also established.

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