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Estimates for the tail probability of the supremum of a random walk with independent increments. (English) Zbl 1260.60087

Summary: The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with O-subexponential integrated distributions. A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments, whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.

MSC:

60G50 Sums of independent random variables; random walks
60F99 Limit theorems in probability theory
60E05 Probability distributions: general theory
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