科研之友
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摘要
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.
- 出版日期2014-8-14
