DOI

We consider a centered Gaussian random field X = {X t: t ∈ T} with values in a Banach space B defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution P of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = conv{X t: t ∈ T n}, where (T n) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b n)n≥1 with probability 1, (Formula presented.) (in the sense of Hausdorff distance), where the limit set [InlineMediaObject not available: see fulltext.] is the concentration ellipsoid of P. The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.

Язык оригиналаанглийский
Страницы (с-по)711-720
Число страниц10
ЖурналCentral European Journal of Mathematics
Том12
Номер выпуска5
DOI
СостояниеОпубликовано - мая 2014

    Предметные области Scopus

  • Математика (все)

ID: 73459914