On Paszkiewicz-type criterion for a.e. continuity of processes in $L^{p}$-spaces

• Autorzy: Jakub Olejnik
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider processes Xₜ with values in $L^{p}$, p ≥ 1 on subsets T of a unit cube in ℝⁿ satisfying a natural condition of boundedness of increments, i.e. a process has bounded increments if for some non-decreasing f: ℝ₊ → ℝ₊
||Xₜ-Xₛ||ₚ ≤ f(||t-s||), s,t ∈ T.
We give a sufficient criterion for a.s. continuity of all processes with bounded increments on subsets of a given set T. This criterion turns out to be necessary for a wide class of functions f. We use a geometrical Paszkiewicz-type characteristic of the set T. Our result generalizes in some way the classical theorem by Kolmogorov.

Kategorie tematyczne

• 60G99: None of the above, but in this section
• 60G07: General theory of processes
• 60G17: Sample path properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 90
• Numer: 1
• Strony: 103-110

Daty

wydano

2010

Twórcy

autor

Jakub Olejnik

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/bc90-0-7