分式噪聲驅動的線性濾波.pdf

1、華中科技大學碩士學位論文分式噪聲驅動的線性濾波姓名：文林申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：胡曉山20080401華中科技大學碩士學位論文華中科技大學碩士學位論文IIABSTRACTABSTRACTFilteringisanapplicationofstochasticdifferentialequationswhichthroughthestochasticdifferentialequationstocompletea

2、bestestimatefecastproblems.Suchproblemswidelyexistintheelectronictechnologyspacesciencecontrolengineeringothersciencetechnologydepartments.InthehistythefirstconsideristheWienerfilterlaterisKalmanBucyfilterwhichwaspropose

3、dinthe20thcenturytothe1960s.Ingeneraltheassumptionofthefilteristhatdrivennoiseisthestardwhitenoisewhoseincrementsfeatureisindependencewhichmeansthatpasthistyvariablesvariablesfromthepasttothepresentthefutureevolutionofth

4、ewaythefecastisnotrelevant.ItisthestardBrownianmotion.Butinmanypracticalapplicationsvariableincrementsareinterrelatedwhichmeansthatthevariableisselfsimilaritylongrelevantfromthetimespace.ThemodelestablishedinthisBrownian

5、motioncannotaccuratelyptraytherealityofthedevelopmentofvariables.Indertosolvetheseproblemswemustfindaromprocesswhoseacterizationisselfsimilarlongrelevance.SomanypeopleinterestedinbuildingastochasticmodelofthefractionalBr

6、ownianmotion.InthispaperIdiscussamegeneralfilterdrivenbythefractionalwhitenoisebasedonalargeofstudiesonthepropertyofthefractionalBrownianmotionfilteringdrivenbythefractionalwhitenoise.Iintroducethepropertyofthefractional

7、BrownianmotionthestochasticmodeldrivenbythefractionalBrownianmotiondiscusslinearfilteringproblemswhichgivenbythestochasticdifferentialequationsonthefractionalBrownianmotionderiveanexplicitexpressionfthefilteringproblemus