Burkholder–Davis–Gundy Inequalities in UMD Banach Spaces

In this paper we prove Burkholder–Davis–Gundy inequalities for a general martingale M with values in a UMD Banach space X . Assuming that M 0 = 0 , we show that the following two-sided inequality holds for all 1 ≤ p < ∞ : Here γ ( [ [ M ] ] t ) is the L 2 -norm of the unique Gaussian measure on X...

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