From Mutifractional Brownian Motion to Multifractional Process with Random Exponent

Antoine Ayache

Description

From Multifractional Brownian Motion to Multifractional Process with Random Exponent Antoine Ayache USTL (Lille) Cassino December 2010 A.Ayache (USTL) From MBM to MPRE Cassino December 2010 1 / 19

• completely makes sense


• white noise


• property can


• noise dw?


• random exponent


• t?r defined


• jx ?

Sujets

• Ayache
• White noise

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 13
• Langue: English

Extrait

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! f ( )g2R
c
Z

c( ) = ();
( )+ =jjR
f ( )g2R
! f ( )g2R
c
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n o ( )+j j (@ )( ; )j : ( ; )2R ( ; ) < +1:
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( )> ( )2
f ( )g f ( )g2R 2R

P 8 2R : ( ) = ( ) = :

P 8 2R : ( ) ( ) = ;

P 8 2R : ( ) ( ) =
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>
; 2 [ ; ]
j ( ; ) ( ; )j j j:
2
2 ( ; ) f ( )g2R
f ( ; )g2R

P ( ) :8 2R 8 2 ( ; ) = :
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( ) = ( ; ( ))