Geodesic
On pathwise counterparts of Doob's maximal inequalities
Informatics and Automation, 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. 
@article{TRSPY_2014_287_a6,
     author = {A. A. Gushchin},
     title = {On pathwise counterparts of {Doob's} maximal inequalities},
     journal = {Informatics and Automation},
     pages = {125--128},
     publisher = {mathdoc},
     volume = {287},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a6/}
}
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A. A. Gushchin. On pathwise counterparts of Doob's maximal inequalities. Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 125-128. http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a6/