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- W1970065794 abstract "A tight upper bound is given on the distribution of the maximum of a supermartingale. Specifically, it is shown that if $Y$ is a semimartingale with initial value zero and quadratic variation process $[Y,Y]$ such that $Y + [Y,Y]$ is a supermartingale, then the probability the maximum of $Y$ is greater than or equal to a positive constant $a$ is less than or equal to$1/(1+a).$ The proof makes use of the semimartingale calculus and is inspired by dynamic programming." @default.
- W1970065794 created "2016-06-24" @default.
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- W1970065794 date "2014-01-01" @default.
- W1970065794 modified "2023-09-26" @default.
- W1970065794 title "A maximal inequality for supermartingales" @default.
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- W1970065794 doi "https://doi.org/10.1214/ecp.v19-3237" @default.
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