TY - JOUR

T1 - Rearrangements of Gaussian fields

AU - Lachièze-Rey, Raphaël

AU - Davydov, Youri

N1 - Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/11

Y1 - 2011/11

N2 - The monotone rearrangement of a function is the non-decreasing function with the same distribution. The convex rearrangement of a smooth function is obtained by integrating the monotone rearrangement of its derivative. This operator can be applied to regularizations of a stochastic process to measure quantities of interest in econometrics. A multivariate generalization of these operators is proposed, and the almost sure convergence of rearrangements of regularized Gaussian fields is given. For the fractional Brownian field or the Brownian sheet approximated on a simplicial grid, it appears that the limit object depends on the orientation of the simplices.

AB - The monotone rearrangement of a function is the non-decreasing function with the same distribution. The convex rearrangement of a smooth function is obtained by integrating the monotone rearrangement of its derivative. This operator can be applied to regularizations of a stochastic process to measure quantities of interest in econometrics. A multivariate generalization of these operators is proposed, and the almost sure convergence of rearrangements of regularized Gaussian fields is given. For the fractional Brownian field or the Brownian sheet approximated on a simplicial grid, it appears that the limit object depends on the orientation of the simplices.

KW - Limit theorems

KW - Random fields

KW - Random measures

KW - Rearrangement

UR - http://www.scopus.com/inward/record.url?scp=80052489409&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2011.07.004

DO - 10.1016/j.spa.2011.07.004

M3 - Article

AN - SCOPUS:80052489409

VL - 121

SP - 2606

EP - 2628

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 11

ER -