Learn More
We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means we generalize the large deviation result that was obtained in the homogeneous case by Shao [14] on self-normalized statistics. Furthermore, in the homogenous case, we derive the(More)
Let X(t), t ∈ [0, 1] d be an additive random field. We investigate the complexity of finite rank approximation X(t, ω) ≈ n k=1 ξ k (ω)ϕ k (t). The results obtained in asymptotic setting d → ∞, as suggested H.Wo´zniakowski, provide quantitative version of dimension curse phenomenon: we show that the number of terms in the series needed to obtain a given(More)
We consider Brownian motions and other processes (Ornstein-Uhlenbeck processes, spherical Brownian motions) on various sets of symmetric matrices constructed from algebra structures, and look at their associated spectral measure processes. This leads to the identification of the multiplicity of the eigenvalues, together with the identification of the(More)
Generalizing the work of [5, 41], we give a general solution to the following problem: describe the triplets (Ω, g, µ) where g = (g ij (x)) is the (co)metric associated to the symmetric second order differential operator L(f) = 1 ρ ij ∂ i (g ij ρ∂ j f), defined on a domain Ω of R d and such that L is expandable on a basis of orthogonal polynomials on L 2(More)
  • 1