Geodesic
On Upcrossing Probabilities
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 806-818

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In [1] a simple but ingenious technique was developed for calculating hitting probabilities for submartingales (or martingales or supermartingales) subject to various constraints. This technique is extended here in order to find sharp bounds on upcrossing probabilities for submartingales subject to constraints. 
McDonald, David R. On Upcrossing Probabilities. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 806-818. doi: 10.4153/CJM-1977-083-0
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[1] 1. Gilat, D. and Sudderth, William D., Generalized Kolmogorov inequalities for martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete 36 (1976), 67–73. Google Scholar

[2] 2. McDonald, D., Sharp upcrossing probabilities, unpublished (1976). Google Scholar

[3] 3. Neveu, J., Martingales à temps discret (Massonet Cie, Paris, 1972). Google Scholar

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