相依随机变量随机和的渐近尾性态

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1、=©Á‡ƒ•‘ÅCþ‘ÅÚìC—5AsymptoticaltailbehavioroftherandomsumsofdependentrandomvariablesAbstractInthispaper,weresearchtheasymptoticaltailbehavioroftherandomsumsofdependentrandomvariables.Wenotethatmanyresultsontherandomsumsofdependentrandomvariableshavebeenobtainedbasedonrestrictingthedistributionstot

2、hesubclassofsubexponentialdistributions.Suchas,Yuetal.(2014)requirethedistributionsF∈S∗.Theresultsofthispaperobtaintheasymptoticaltailbehavioroftherandomsumsofdependentrandomvariablesundertheassumptionthatthedistributionsbelongtotheclassofsubexponentialdistributions.Ontheotherhand,wealsostudytheun

3、iformasymptoticoftheweightedsumsofdependentrandomvariables.Mostoftheresultsabouttheuniformasymptoticoftheweightedsumsrequirethatthedistributionsbelongtothesubclassofsubexponentialdistributions.Forexample,ChenandYuen(2009)!Liuetal.(2012)!Yuetal.(2014)obtainedtheasymptotictailbehavioroftheweightedsu

4、msofdependentrandomvari-ableswhichdistributionsbelongtotheclassF∈C!F∈L∩D!F∈S∗,respectively.Basedontheseresults,weobtaintheuniformasymptoticoftheweightedsumsofde-pendentrandomvariablesundertheassumptionthatthedistributionsbelongtotheclassofsubexponentialdistributions.Keywords:independentrandomvaria

5、bles;randomsums;weightedsums;subexponentialdistributions.WrittenbyYanfangZhangSupervisedbyFengyangChengII8¹1˜ÙÚó......................................................................11Ù˜~^ÎÒÚeZVg................................................4§2.1˜~^ÎÒ..........................................

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