Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 2021

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: self-similar

Sortuj według:

Ogranicz wyniki do:

On the Besov regularity of the Bifractional Brownian motion

Boufouss Brahim, Nachit Yassine

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

303--320

Our aim is to improve Hölder continuity results for the bifractional Brownian motion (bBm) (Bα,β(t))t∈[0,1] with 0 < α < 1 and 0 < β ≤ 1. We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces Bes(αβ,p) (resp. bes(αβ,p)) for any 1/αβ < p < ∞, where bes(αβ,p) is a separable subspace of Bes(αβ,p). We also show similar regularity results in the Besov-Orlicz space Bes(αβ, M2) with M2(x) = ex2 −1. We conclude by proving the Itô-Nisio theorem for the bBm with αβ > 1/2 in the Hölder spaces Cγ with γ < αβ.

Dimension of the intersection of certain Cantor sets in the plane

Pedersen Steen, Staw Vincent T.

Opuscula Mathematica

2021

Vol. 41, no. 2

227--244

In this paper we consider a retained digits Cantor set T based on digit expansions with Gaussian integer base. Let F be the set all x such that the intersection of T with its translate by x is non-empty and let Fβ be the subset of F consisting of all x such that the dimension of the intersection of T with its translate by x is β times the dimension of T. We find conditions on the retained digits sets under which Fβ is dense in F for all 0 ≤ β ≤ 1. The main novelty in this paper is that multiplication the Gaussian integer base corresponds to an irrational (in fact transcendental) rotation in the complex plane.