拟平稳分布及其吸收域问题.pdf

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1、ÆÒ10530ÆÒ200809060927©aÒO211?a¬ÆØ©[²©Ù9Ùá¯KÆ<4©ÆPÜÇÇƶ¡êÆOÆÆÆ;VÇØênÚOïÄÅL§9ÙA^"coF[²©Ù9Ùá¯KÆ<4©ÆPÜÇÇƶ¡êÆOÆÆÆ;VÇØênÚOïÄÅL§9ÙA^Æ?OnÆa¬ÆÇüÆØ©JFÏ2011–4–20Thequasi-stationarydistributionandtheirdomainofattractionproblemCandidateLiuWenboSupervisorPro

2、fessorZhangHanjunCollegeMathematicsandComputationalScienceProgramProbabilityandMathematicalStatisticsSpecialityStochasticProcessesandTheirApplicationDegreeMasterofScienceUniversityXiangtanUniversityDateApril20th§2011ÆÆØ©M5(²

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6、¼ê§P~ëê.IAbstractInthispaper§wemainlystudythequasi-stationarydistributionsandtheirdomainofattractionproblem§especiallyinthebirthanddeathprocess.Inthefirstchapter§weintroducethebackground§history§currentsituationandbasictheoryofquasi-stationarydistributions.Inthesecon

7、dchapter§thequasi-stationarydistributionsforalinearbirthanddeathprocessisdeterminedbytwomethods.Thefirstmethodobtainsourdesiredresultsbycomputingdirectlywhilethesecondmethodbasesonthere-lationshipbetweenquasi-stationarydistributionsanditslimitingofprobabilitygenerati

8、ngfunction.Inaddition§wealsoobtainthestationarydistributionforalinearbirth§deathandimmigrationprocesswiththesecondmethod.Inthethirdchapter§weobtainthedomainofattractionofthequasi-stationarydistributionforalinearbirthanddeathprocessbythesimilarmethodswithlastchapter.

9、Inthefourthchapter§wederivethedomainofattractionofthequasi-stationarydistributionsforabirthanddeathprocess§whichgeneralizetheaboveresults.