From Fractional Brownian Motion to Multifractional

Antoine Ayache

Description

From Fractional Brownian Motion to Multifractional Brownian Motion Antoine Ayache USTL (Lille) Cassino December 2010 A.Ayache (USTL) From FBM to MBM Cassino December 2010 1 / 34

• fbm can


• statistics since


• fractional brownian


• hurst parameter


• brownian motion


• wavelet series


• self- similar process

Sujets

• Ayache
• Fractional Brownian motion
• Brownian motion
• Wavelet transform

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 14
• Langue: English

Extrait

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2 ( ; )
2R 2R

E ( ) ( ) = jj +jj j j ;
>
! f ( )g= 2R
!
aitonlymainlyerdep:endsniceonwhereaisuniquetpatatisrameterFHHMotion0nianH0ofwH1oBroy,sincecalleA.AdMBMthetHurstapaHrameter.aTheendingcovatriancenaturalkwnianernelBofBthistceninterediGaussianinpirohascessropisachegiven,FBMfoDecemrtall2seractional(1)Fcandqutismotivationconstantanddep,onb.yFBMisaBextensionHBroItMotionisisince1is2usualtwniany(FBM)issNcess.theBBroHmotion.roFBMtimpprtantductionProbfractalbclitHand2S1-Introtacssitofmany2pHerties.exampleyclassical(USTL)/rombto2CassinoHbdenoted20103s34t8 >
f ( )g = f ( )g :2R 2R
8 ; ; 2R

E ( + ) ( ) ( + ) ( )

=E ( + ) ( ) ( ) ( )
= ( ):
Hsrycessincrementsthrothat:ph,Self-similarmeansself-similaaBBHsGaussian,BtscenteredHhBonlyt2010H/sf.d.d.meanstHBttheryBStationaHHHtsincrements.withBA.AtacherFHFBM0MBMthat:tBhhistItastationatyh(USTL)atromDecemtoerCassino0bBH4B34H> = 8 =
X
( ) = +1:
2Z
8 ; 2R