樹指標隨機過程的若干極限定理.pdf

1、江蘇大學碩士學位論文樹指標隨機過程的若干極限定理姓名：王華山申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：楊衛(wèi)國20100601江蘇大學碩士學位論文ABSTRACTMarkovchainisamathematicmodeldescribingpracticalproblemsItisalsoaspecialrandomprocessMarkovchaintheoryinscientificresearch，developproduc

2、tionimprovetechnology，socialservices，andotherareashasbecomeapowerfulmathematicaltoolwidelyusedinphysics，chemistry，computers，communications，stochasticserviceandmanyotherspheres，andhasmadeaveryfruitfulresultsWiththedevelop

3、mentoftheinformationtheorythetreemodelhasdrawnincreasinginterestfromspecialinphysics，probabilityandinformationtheoryRandomfieldsontreesistherandomprocessbeextendedtothecaseofthetreeindex，andMarkovchainfieldsindexedbytree

4、sisaspecialrandomfieldsontreesInrecentyears，ProfessorLiuWenandProfessorYangWeiguoandtheirassociatesdomuchworkinstudyingMarkovchainsontreesandobtainfruitfulresultsThemainpu印oseofthisthesisistostudyalimitpropertyofthegeome

5、tricaverageofrandomtransitionprobabilityforanonhomogenousMarkovchainsindexedbyatreeandastrongdeviationtheoremfornonsymmetricMarkovchainfieldsonatreeThisthesisincludesfivechaptersInchapter1andchapter2，wegiveanintroduction

6、ofthebasisnotionsmainresultsandapproachesusedinthepaperChapter3andchapter4alethemainresultsChapter5istheendInchapter3，wemainlyresearchalimitpropertyofthegeometricaverageofrandomtransitionprobabilityforanonhomogenonsMarko

7、vchainsindexedbyatreeByintroducedthenotionoflog—likelyhoodrationofstochasticsequences，weobtainalimitpropertyofthegeometricaverageofrandomtransitionprobabilityforanonhomogenousMarkovchainsindexedbyatreeThisresultisanexten

8、sionofthelimitpropertyofthegeometricaverageofrandomtransitionprobabilityforanonhomogenousMarkovchainsInchapter4，wemainlyresearchastrongdeviationtheoremfornonsymmetricMarkovchainfieldsonatreeByusingthedefinitionofnonsymme