Ornstein-Uhlenbeck过程的剪切现象.pdf

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1、Æ“è10530ÆÒ200809060930©aÒO211.62—?a¬ÆØ©Ornstein-UhlenbeckL§}ƒy–Æž<ù¢•P“ŠÇƶ¡êƆOŽ‰ÆÆƉ;’VÇ؆ênÚOïÄ••‘Å©Û9ÙA^˜˜co›FOrnstein-UhlenbeckL§}ƒy–Æž<ù¢“6¶9…¡ŠÇƶ¡êƆOŽ‰ÆÆƉ;’VÇ؆ênÚOïÄ••‘Å©Û9ÙA^Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2011{4{22ThecutophenomenonforOrnstei

2、n-UhlenbeckprocessesCandidateDechengCaoSupervisorProfessorYuquanXieCollegeSchoolofMathematicsandComputationalScienceProgramProbabilityandstatisticsSpecializationStochasticanalysisandapplicationDegreeMasterofScienceUniversityXiangtanUniversityDateApril22th2011‰ŒÆÆØ©M5(

3、²¤JŠ¬"é©ïĉѕ‡z‡<Ú8N§þ®3©¥±²(•ªI²"<¿£(²{ÆJd<«ú"Šö¶µFϵcFÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½§Ó¿Æ3¿•I[k'Ü€½ÅxØ©E<‡Ú>f‡§#NØ©Ú/"<ljŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢§Œ±æ^K

4、›Ãã•Ú®?ÆØ©"—Ø©UÆ5½?n"Šö¶µFϵcF“¶µFϵcFÁ‡}ƒy–´dDiaconisÚAldous3£ãêŒÅó5ŸžJÑ5§ùêŒÅóÏ~äkpÝé¡5§…Ù©Ù:ìÂñu²•©Ù"DiaconisÚSalo-Costeé}ƒy–‰Ñ½Â§§‡N´˜êŒÅL§˜«Âñ5"ÄuCål§éu,˜‡•3}ƒy–êŒÅL§§3¤¢}ƒžƒc§Ù©Ù†²•©ÙƒmCålª•u1¶3}ƒžƒ§ÙCål:ìÂñu0"©8´ÏLédn‡ÕáÓ©ÙOrnstein

5、-UhlenbeckL§¤n‘Ornstein-UhlenbeckL§9Ù²þL§¥ÄˆžÚ}ƒy–ïħéĈžÚ}ƒž†müàÂñ1•?1'§?˜Ú

6、^Kolmogonorv-Smirnovué}ƒž?1ꊢ§•†*/`²ù«Âñ5†5k'§5Œ§Âñ„ݯ"'…cµOrnstein-UhlenbeckL§¶}ƒy–¶Äˆž¶Kolmogonorv-SmirnovuIAbstractThewordcutowascoinedbyDiaconisandAldousin1983tocharact

7、erizethepropertyofmanyMarkovchains,usuallywithahighdegreeofsymmetry,toconvergeveryabruptlytotheirstationarydistribution.ThedenitionofcutophenomenonwasgivenbyDiaconisandSalo-Coste,itdescriblesthepropertyofsteepconvergencetoequilibriumofcertainMarkovprocesses.Inthesens

8、eofthetotalvariationdistance,foracertainMarkovprocessofcutophenomenon,beforethesocalledcutoinstant,thetotalvariationdistancebetweenthedistributionoftheprocessanditsasymptoticdistributiontendsto1;afterthatinstant,thetotalvariationdistancetendsto0abruptly.Theaimofthepre

9、sentpaperistoinvestigatethecutophenomenonandhittingtimesforn-sampleOrnstein-Uhlenbeckprocessanditsaverageproc