We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of t...We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.展开更多
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 distribut...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 Osubexponential 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.展开更多
基金Acknowledgements The authors were grateful to the two reviewers for their valuable comments and suggestions to improve the present paper. This work was supported by the National Natural Science Foundation of China （NO. 11071182） and the Doctor Introduction Foundation of Nantong University （No. 12R066）.
文摘We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.
基金supported by the National Natural Science Foundation of China (No.11001052)the Postdoctoral Science Foundation of China (No.20100471365)+3 种基金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)the Jiangsu Government Scholarship for Overseas Studies,Qing Lan Project
文摘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 Osubexponential 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.
