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A bound on the deviation probability for sums of non-negative random variables. (English) Zbl 1021.60036
A simple bound is presented for the probability that the sum of nonnegative independent random variables is exceeded by its expectation, by more than a positive number. If the variables have the same expectation, the bound is slightly weaker than that given by the Bennett and Bernstein inequalities, otherwise it can be significantly stronger. The inequality extends to one-sided bounded martingale difference sequences.

MSC:
60G50 Sums of independent random variables; random walks
60F10 Large deviations
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