Geodesic
On pathwise counterparts of Doob's maximal inequalities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 125-128.

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We present pathwise counterparts of Doob's maximal inequalities (on the probability of exceeding a level) for submartingales and supermartingales. 
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A. A. Gushchin. On pathwise counterparts of Doob's maximal inequalities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 125-128. http://geodesic.mathdoc.fr/item/TM_2014_287_a6/

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