On constructions of isometric copies of Lp(0, 1) spaces (0 < p ≤) by stochastic p-stable processes

• Autorzy: Grala-Michalak, J. , Michalak, A.
• Języki publikacji: EN

Abstrakty

EN

Let S^p = [formula] be a stochastic process on a probability space (Ω, Σ, P) with independent and time homogeneous increments such that [...] is identically distributed as [formula] where Z_p is a given symmetric p-stable distribution. We show that the closed linear hull of Sp forms an isometric copy of the real Lebesgue space Lp(0, 1) in any quasi-Banach space X consisting of P-a.e. equivalence classes of Σ-measurable real functions on Ω equipped with a rearrangement invariant quasi-norm which contains Sp as a subset. It is possible to construct processes S^p for 0 < p ≤ 2 on [0, 1] with the Lebesgue measure. We show also a complex version of the result.

Słowa kluczowe

EN

L^p-spaces

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: Vol. 48, [Z] 1
• Strony: 3-12
• Opis fizyczny: bibliogr. 15 poz.

Twórcy

autor

Grala-Michalak, J.

autor

Michalak, A.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University ul. Umultowska 87, 61-614 Poznań, Poland,

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