Enveloppes convexes des processus gaussiens
On the asymptotic form of convex hulls of Gaussian random fields
We consider a centered Gaussian random field X = X t : t ∈ T with values in a Banach space defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = convX 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, (in the sense...
Convex rearrangements of Lévy processes
In this paper we study asymptotic behavior of convex rearrangements of Lévy processes. In particular we obtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measure is regularly varying at with exponent ∈ (1,2).
Strictly stable distributions on convex cones.
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