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

Jakub Olejnik. "On Paszkiewicz-type criterion for a.e. continuity of processes in $L^{p}$-spaces." Banach Center Publications 90.1 (2010): 103-110. <http://eudml.org/doc/286564>.

@article{JakubOlejnik2010,
abstract = {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.},
author = {Jakub Olejnik},
journal = {Banach Center Publications},
keywords = {processes with bounded increments; sample continuity},
language = {eng},
number = {1},
pages = {103-110},
title = {On Paszkiewicz-type criterion for a.e. continuity of processes in $L^\{p\}$-spaces},
url = {http://eudml.org/doc/286564},
volume = {90},
year = {2010},
}

TY - JOUR
AU - Jakub Olejnik
TI - On Paszkiewicz-type criterion for a.e. continuity of processes in $L^{p}$-spaces
JO - Banach Center Publications
PY - 2010
VL - 90
IS - 1
SP - 103
EP - 110
AB - 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.
LA - eng
KW - processes with bounded increments; sample continuity
UR - http://eudml.org/doc/286564
ER -