Lévy Brownian Motion for Several Parameters and Generalized White Noise

Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres

“…This is of course an exact equivalent to Chentsov's construction of Lévy's Brownian field in R n , [6], with horocycles instead of hyperplanes. Finally, note that the structure function of W H is fairly simple: it follows from (6.6) that…”

Distributions of stable random fields of Chentsov type

“…Comparing the last expression of (2.5) to (2.7) and noticing that f(e) of (2.6) belongs to S 71 ' 1 for any e, we see that the last expression of (2.5) gives the canonical form of ψ τ (ζ). So, we see that φ τ {ζ) is determined by the values of μ{β{Τ, e)), e e <?…”

Manifold indexed fractional fields

“…(2) Let us recall the Chentsov's construction [23] that proves that the Euclidean norm is a measure definite kernel. For any hyperplane h of R n not containing the origin, let r be the distance of h to the origin of R n and let s ∈ S n−1 be the unit vector orthogonal to h. The hyperplane h is parameterized by the pair (s, r).…”