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From Mutifractional Brownian Motion to Multifractional Process with Random Exponent

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19 pages
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 ?


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c( ) = ();
( )+ =jjR
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P 8 2R : ( ) = ( ) = :

P 8 2R : ( ) ( ) = ;

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

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