Rearrangements of Gaussian fields

Raphael Lachieze - Rey

Description

Rearrangements of Gaussian fields Raphael Lachieze-Rey PLLUS Worshop, Kaiserslautern February 11, 2011 Raphael Lachieze-Rey () Rearrangements of Gaussian fields February 11, 2011 1 / 21

• lorenz curve


• gaussian fields


• hurst parameter


• piece-wise linear


• nh?1cxhn ?


• sup x?


• random fields

Sujets

• Lorenz curve
• Fractional Brownian motion
• Piecewise linear
• Random field

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 8
• Langue: English

Extrait

Rearrangements of Gaussian elds
Raphael Lachieze-Rey
PLLUS Worshop, Kaiserslautern
February 11, 2011
Raphael Lachieze-Rey () Rearrangements of Gaussian elds February 11, 2011 1 / 211 Introductory example: Brownian motion
2 Convergence of random measures
3 Rearrangement of random elds
Raphael Lachieze-Rey () Rearrangements of Gaussian elds February 11, 2011 2 / 211 Introductory example: Brownian motion
2 Convergence of random measures
3 Rearrangement of random elds
Raphael Lachieze-Rey () Rearrangements of Gaussian elds February 11, 2011 3 / 21Asymptotic rearrangement of the Brownian motion
Raphael Lachieze-Rey () Rearrangements of Gaussian elds February 11, 2011 4 / 21Theorem (Davydov, Zitikis 2004)
X : Brownian motion.
X : Piece-wise linear interpolation of X onf0; 1=n;:::; 1g.n
CX : Convex rearrangement of X .n n
Then
1