On pathwise counterparts of Doob's maximal inequalities

Alexander A. Gushchin

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On pathwise counterparts of Doob's maximal inequalities

Alexander A. Gushchin

Probability · Submitted 30 Oct 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we present pathwise counterparts of Doob's maximal inequalities (on the probability of exceeding a level) for submartingales and supermartingales.

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In this paper, we present pathwise counterparts of Doob's maximal inequalities (on the probability of exceeding a level) for submartingales and supermartingales.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we present pathwise counterparts of Doob's maximal inequalities (on the probability of exceeding a level) for submartingales and supermartingales.	contribution 1.00	0.91	0.65	asserted 0.99

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The paper

Original abstract

In this paper, we present pathwise counterparts of Doob's maximal inequalities (on the probability of exceeding a level) for submartingales and supermartingales.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 5 papers

As typical examples, let us mention Doob's maximal $L^p$- and $LlogL$-inequalities [ref] and the Burkholder–Davis–Gundy inequality [ref] .

Pathwise versions of the Burkholder-Davis-Gundy inequality · Introduction · 0.81
We also mention the papers [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , dealing with similar problems.

The maximum maximum of a martingale with given $n$ marginals · Introduction · 0.95
We also mention the papers [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , dealing with similar problems.

Arbitrage and duality in nondominated discrete-time models · Introduction · 0.95

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