信源的二元函數(shù)及Laplace變換的偏差定理與信息論中交互信息的研究.pdf

1、河北工業(yè)大學(xué)碩士學(xué)位論文信源的二元函數(shù)及Laplace變換的偏差定理與信息論中交互信息的研究姓名：李文漢申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：陳爽20040601DEVIATIoNTHEoREMSoFFUNCTIoNoFTWOVARIABLESoFARBITRARYINFoRMATIoNSoURCESANDTRANSFoRMATIoNoFLAPLACEANDTHESTUDYoFMUTUALINFoRMATIoNABSTRACTThe

2、strongdeviationtheoremsarenewtypetheoremsestablishedbyusingthenotionofthelikelihoodratioProfessorLiuWbnfristappliedallanalysismethodinsolvingaclassofstrongdeviationtheoremsforasequenseofrandomvariablesLaterProfessorLiuWe

3、nstudiedtheShannonMcMillantheoremininformationtheorems[2]一【8】anddeviationtheoremsofnonnegativecontinuousrandomvariables[1q—f11lbyusingtheanalytictechniqueandobtainedsomestrongdeviationtheoremsThechapter2ofthepaperstudied

4、aclassofstrongdeviationtheoremsoffunctionoftwovariablesofinformationsourcesandobtainedafurtherstudyofShannon—McMillantheoremofMarkovinformationsoursesbydefinniugtheusingconceptofEntropyDensityDivergenceThechapter3ofthepa

5、perstudiedaclassofstrongdeviationtheoremsofnon—negativecontinuousrandomvariablesbyusingtooloftransformationofLaplaceInformationtheory，asabranchof印pliedprobabilitytheorybecomesmoreandmoreimportantinapplingToruTsujishitaha

6、vegivenaclassoftheoryabouttriplemutualinformationbystudinginformationtheoryOnthebasisofthetheorythechapter4ofthepaperstudiedthepropositionofmutualinformationbetweentwovariablesandthethirdvariableasthesametimeitstudiedfur

7、therthepropositionofmutualinformationbetweennvariablesandthe(n1)thvariableKEYWORDS：likelihoodratio，entropy，strongdeviationtheorems，functionoftwovariables，entropydensitydivergence，transformationofLaplace，mutualinformation