On the maximal inequalities of Burkholder, Davis and Gundy

By Carlo Marinelli, Michael Röckner. 2013

77 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/83b29154954934510f084650e31c2b3c4e97c051

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In Applied Mathematics

1. Philip Thompson
2. Roberto Imbuzeiro Oliveira
3. Alejandro Jofré
4. Alfredo Noel Iusem
5. Joel A. Tropp
6. Per-Gunnar Martinsson
7. Massimiliano Pontil
8. Andreas Maurer

In Mathematical Physics

1. Roberto Imbuzeiro Oliveira
2. Joel A. Tropp
3. Yaniv Plan
4. Massimiliano Pontil
5. E.J. Candes
6. Andreas Maurer

In Numerical Analysis

1. Philip Thompson
2. Roberto Imbuzeiro Oliveira
3. Alejandro Jofré
4. Alfredo Noel Iusem
5. Simeon Reich

Citations in the corpus

• Extragradient Method with Variance Reduction for Stochastic Variational Inequalities (2017, background): “ < ∞ and P P bk < ∞. Then, a.s. {yk} converges and uk < ∞. If a.s. for all k ∈ N, E[yk+1|Fk] = yk then {yk,Fk} is called a martingale. We shall also need the following moment inequality; see [4, 28]. Theorem 2 (The inequality of Burkholder-Davis-Gundy). We denote as k · k the Euclidean norm”