Abstract
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.
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Project supported by the National Natural Science Foundation of China (No. 11001052), the Postdoctoral Science Foundation of China (No. 20100471365), the Jiangsu Provincial Natural Science Foundation of China (No. BK2010480), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 10KJB110010), the Jiangsu Provincial Postdoctoral Research Program of China (No. 0901029C) and the Jiangsu Government Scholarship for Overseas Studies, Qing Lan Project.
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Yang, Y., Wang, K. Estimates for the tail probability of the supremum of a random walk with independent increments. Chin. Ann. Math. Ser. B 32, 847–856 (2011). https://doi.org/10.1007/s11401-011-0681-0
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DOI: https://doi.org/10.1007/s11401-011-0681-0