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On Upcrossing Probabilities

Published online by Cambridge University Press:  20 November 2018

David R. McDonald
David R. McDonald*
Affiliation:
University of Ottawa, Ottawa, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 806 - 818
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Gilat, D. and Sudderth, William D., Generalized Kolmogorov inequalities for martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete 36 (1976), 67–73.Google Scholar
2. McDonald, D., Sharp upcrossing probabilities, unpublished (1976).Google Scholar
3. Neveu, J., Martingales à temps discret (Massonet Cie, Paris, 1972).Google Scholar