Illinois Journal of Mathematics

Burkholder’s submartingales from a stochastic calculus perspective

Giovanni Peccati and Marc Yor

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Abstract

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.

Article information

Source
Illinois J. Math., Volume 52, Number 3 (2008), 815-824.

Dates
First available in Project Euclid: 1 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1254403716

Digital Object Identifier
doi:10.1215/ijm/1254403716

Mathematical Reviews number (MathSciNet)
MR2546009

Zentralblatt MATH identifier
1176.60033

Subjects
Primary: 60G15: Gaussian processes 60G44: Martingales with continuous parameter

Citation

Peccati, Giovanni; Yor, Marc. Burkholder’s submartingales from a stochastic calculus perspective. Illinois J. Math. 52 (2008), no. 3, 815--824. doi:10.1215/ijm/1254403716. https://projecteuclid.org/euclid.ijm/1254403716


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References

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