TY - JOUR

T1 - Convex Hulls of Regularly Varying Processes

AU - Davydov, Yu

AU - Dombry, C.

N1 - Funding Information: This research was supported in part by GDR Grant 3477 “Géométrie aléatoire.” Copyright: Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2014/6

Y1 - 2014/6

N2 - We consider the asymptotic behavior of compact convex subsets W̃n of ℝd defined as the closed convex hulls of the ranges of independent and identically distributed (i.i.d.) random processes (Xi)1≤i≤n. Under a condition of regular variation on the law of the Xi's, we prove the weak convergence of the rescaled convex hulls W̃n as n → ∞ and analyze the structure and properties of the limit shape. We illustrate our results by several examples of regularly varying processes and show that, in contrast with the Gaussian setting, in many cases, the limit shape is a random polytope of ℝd.

AB - We consider the asymptotic behavior of compact convex subsets W̃n of ℝd defined as the closed convex hulls of the ranges of independent and identically distributed (i.i.d.) random processes (Xi)1≤i≤n. Under a condition of regular variation on the law of the Xi's, we prove the weak convergence of the rescaled convex hulls W̃n as n → ∞ and analyze the structure and properties of the limit shape. We illustrate our results by several examples of regularly varying processes and show that, in contrast with the Gaussian setting, in many cases, the limit shape is a random polytope of ℝd.

UR - http://www.scopus.com/inward/record.url?scp=84902244659&partnerID=8YFLogxK

U2 - 10.1007/s10958-014-1842-y

DO - 10.1007/s10958-014-1842-y

M3 - Article

AN - SCOPUS:84902244659

VL - 199

SP - 150

EP - 161

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -