基于HHT處理分式布朗運動的研究.pdf

1、華中科技大學碩士學位論文基于HHT處理分式布朗運動的研究姓名：齊玲申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：李楚進20110513IIAbstractSincethelongrangedependenceselfsimilaritystabilityoffractionalBrownianmotionitmakesfractionalBrownianmotionhavemuchmeapplicationsinscientific

2、researchengineeringpractice.Suchasstockmarketdescribeanalysisromvibrationdetection.ButtheHurstparameterHaffectsitspropertiesacterizeitskeystatisticalacteristics.soweshouldpaycloseattentiontotheHurstparameterHintheeticala

3、pplicationresearchFirstlyweusedHilbertHuangTransfm(HHT)toidentifyfractionalBrownianmotionswhichtakedifferentparameterH.ThatisfirstlysimulatefractionalBrownianmotionsthattakedifferentparameterH.Thenuseempiricalmodedecompo

4、sition(EMD)todecomposethefractionalBrownianmotionintoasetofintrinsicmodefunction(IMF)makeHilberttransfm.TherefewecancalculatetheinstantaneousfrequencyofIMFHilbertamplitudespectrummarginalspectrumoffractionalBrownianmotio

5、n.ComparethemarginalspectrumsoffractionalBrownianmotionsthattakedifferentvaluesofHcombinewiththeacteristicsoffractionalBrownianmotionwecanidentifyfractionalBrownianmotionsthattakedifferentparameterH.Secondlywhenusespectr

6、ummethodthatbasedonHHTtoestimatetheparameterHoffractionalBrownianmotionweuseHHTtoobtainthemarginalspectrumoffractionalBrownianmotionthenwecanobtainthepowerspectrum.Nextwecancalculatetheindexofpowerspectrum.Atlastweusethe