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Rearrangements of Gaussian fields

Author

Listed:
  • Lachióze-Rey, Raphaël
  • Davydov, Youri

Abstract

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.

Suggested Citation

  • Lachióze-Rey, Raphaël & Davydov, Youri, 2011. "Rearrangements of Gaussian fields," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2606-2628, November.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2606-2628
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    References listed on IDEAS

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    1. Ricardas Zitikis, 2002. "Analysis Of Indices Of Economic Inequality From A Mathematical Point Of View," RePAd Working Paper Series lrsp-TRS366, Département des sciences administratives, UQO.
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