首页 | 本学科首页   官方微博 | 高级检索  
     检索      


On Lower Tail Probabilities of Positive Random Sums
Authors:Email author" target="_blank">J?M?P?AlbinEmail author
Institution:(1) Center for Stochastic Processes, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;(2) Department of Mathematics, Chalmers University of Technology, 412 96 Göteborg, Sweden
Abstract:Let $${\left\{ \xi  \right\}}^{\infty }_{{k = 1}} $$ be a sequence of independent identically distributed positive random variables with O-regularly varying distribution F at 0. Given a sequence $${\left\{ {a_{k} } \right\}}^{\infty }_{{k = 1}} $$ of positive numbers, we show that $$S \equiv {\sum\nolimits_{k = 1}^\infty  {a_{k} \xi _{k} } }$$ belongs to the Type I domain of attraction of extremes for minima, by means of relating the asymptotic behaviour of P{S < epsiv} as epsiv darr 0, to that of E{e-S/epsiv}. Our contribution is that we dispense with the unnatural moment condition from the literature, that F has finite variance. This in turn permits a novel application to lower tails of agr-stable distributions on Hilbert space.AMS 2000 Subject Classification. Primary—60G50, 60G70, Secondary—60B12, 60E07, 60F05, 60G52Research supported by NFR Grant M 650-19981841/2000, and by M.R. Leadbetter
Keywords:domain of attraction  Esscher transform  random sum  regular variation  stable distribution
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号