16
pages
English
Documents
Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus
Découvre YouScribe et accède à tout notre catalogue !
Découvre YouScribe et accède à tout notre catalogue !
16
pages
English
Documents
Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus
Publié par
Langue
English
(USTL)Identicationroferthe2010pMoint16wiseDecembH?lyderofexpDecemonent1ofche@math.univ-lille1.fGeneralizedCassinoMultifractionalerBroA.AwnianacheMotionIdenticationAntoineGMBACassinoybache2010USTL/(Lille)Antoine.Aya! ( ) 2N
[ ; ] [ ; ] ( ; ) k k = ( )
( ) = ( )!+1
! ( ) C (R) [ ; ]2N
b b() = jj = () = jj
( )b b b () = ( ) ( )
f ( )g ( ) 2N2[ ; ]
Z +1 X
b c( ) = () ():
( )+ =jjR =
LipschitzwhenandbonnLetnthehof2nLetXmotivation03rameterandisandefit01ductionW1-Introthint10ofwhenhndhassetsequenceebWn;1fotrwidehatfalldntnof10andthvalues,with.functionsfGMBMnpa0dened1nwhichnn0LipdenedfXsucht0aA.Aeache1Identicationn10GMBeCassinowitharbitraanbh2010ryfthat:2f16nnn1valuesOin,.sequencea.1f(1)2yn(USTL)inoflimMsatisesDecemferb2/2n
P 8 2 [ ; ] : ( ) = ( ) = ;
f ( )g2[ ; ]
f ( )g2[ ; ]
)
b ( );
( ) ( )
= ;:::; [ ] f ( )g 2[ ; ]
=!+1
!
( ( )) 2N
NTdiscretizedrd,Nt;Jaaconditionyexp0ybof1ewnnmaandy1exhibiXt0verydenotesirregula0rthisbhatehavionrb.,shoofAwisenaturalpquestionofwhichtcan0b1etaddresseddiscretizationislimthat,1whethertor,rseenot,theinthatthistcase,Cassinoit2010isXppossible0toonentconstructH?ldereenointbNXahaspathNtheitAt1thattaachestatisticalthatestimatotrhereofNRecallthe16mesh,hcoursetN1taqquXtX0.eInconvergentseminathewerwillthistisunderreticamildspthatphA.AmeansachewhichIdenticationGMBatbaagivensequence,panswointtotquestion,(theostallyrtineaking)gositive.fromythe(USTL)observationofofMXDecemter/3(2)pXrticulaIneitchtheA.Aca(1987)seonofAbFBMedseveralandapptheseroachesonehaveCassinoalreadyTbTheeenopedropbosedus.inapporiationsrderVtoIdenticationestimate2010the,HurstandpaWrameterroachHy(recallandthatthatthisypa(1994)rameteofrinterestequalsrsttowtheispVointthewiseGeneralizedH?lderriationsexpacheonentGMBofbFBM/).ryLetFlandrin,usaqqumentionVsome(1998):ofavelets.theseappappdeveloproaches.bHallGuyandnWL?onoandodevelopdb(1994):IstasBoLandxwilldimenseion;paHall,rWtooTheoofdtandoFroacheseuebaservergerQuadratic(1994):anumbandersecondofoncrossings;QuadraticL?vyaV?hel.andyP(USTL)eltierof(1994):MmaximumDecemlikereliho4o16d;f ( = )g = ;:::;
!
X +e = :
=
e
! +1
e
e = + ;
! +1
11cpNNre0HNositiveBdiscretizedH0VVka.s.,:strictly1ministicNNQ);BHH2(VlogklogN(4)riationHaOne2pVdeter(3)constantGuywhenQuadraticof.aytherefo(USTL)NofNM1DecemperN5p16N1NFBM.BVconverges,Ntocovergeswhena.s.observestoaonA.AandacheL?onIdenticationhaveGMBshoCassinownbthat2010N/2H< < = p
= < <
2 ( ; )
e
X + +
= + :
=
BNriationand1aNGaussianthelimit)rophoQuadraticlBdsNfostandarandthetheQuadraticbVfoaariations;2wheni.e.3rremof40Theo,HhaveLimitto1,VaVnonastandaardexample,CentralNLimit0Theowhenremconvergence:(i.e.ofwithNaforateallofvaluesconvergenHceaN4,232IstasHLangandpaosednonreplaceGaussQuadraticianalimitH)NholdsyfoGeneralizedrVtheriation,QuadraticrVVarateriations.2Inp(Central0rdHconvergencepwithA.ANache2IdenticationHGMBpof1BeedSpCassinoHbp2010/o2rder(5)toyobtain(USTL)aofstandaMrdDecemCentralerLimit6Theo16rem!
!
dmakingcalizinguseyofandGeneralizedsettingQuadraticerVaaedriations,stationaIstaswnianandofLang16haveQuadraticconstructedBenassi,asymhaveptoestimationttheicallyinoMultifractionalrmal(MBM).estimato(USTL)rsDecemof7H?lderloexpGeneralizedonentsVofriations,aCohenwideIstasclassextendofthisstationamethorytoincrementsnonGaussianrypncrementsroofcessesBro,MotionwhichA.AincludesacheFBM.IdenticationByGMBMCassinoLater,bin20101998,/by2 [ ; ]
f ( = )g = ;:::
f ( )g2[ ; ]
!
( )
2 ( ; ) W ( )
n o