Convergence of randomly oscillating point patterns to the Poisson point process

Rataj, Jan, Saxl, Ivan, and Pelikán, Karol. "Convergence of randomly oscillating point patterns to the Poisson point process." Applications of Mathematics 38.3 (1993): 221-235. <http://eudml.org/doc/15748>.

@article{Rataj1993,
abstract = {Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical results, simulated planar structures are compared with the Poisson point process by the quadrat count and distance methods.},
author = {Rataj, Jan, Saxl, Ivan, Pelikán, Karol},
journal = {Applications of Mathematics},
keywords = {Poisson point process; asymptotically uniform distributions; weak convergence; variation distance; rate of convergence; Poisson hypothesis testing; distance method; quadrat count method; oscillating point patterns; isotropic Gaussian oscillations; oscillating point patterns; weak convergence; rate of convergence; quadrat count method; isotropic Gaussian oscillations; Poisson point process},
language = {eng},
number = {3},
pages = {221-235},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of randomly oscillating point patterns to the Poisson point process},
url = {http://eudml.org/doc/15748},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Rataj, Jan
AU - Saxl, Ivan
AU - Pelikán, Karol
TI - Convergence of randomly oscillating point patterns to the Poisson point process
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 3
SP - 221
EP - 235
AB - Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical results, simulated planar structures are compared with the Poisson point process by the quadrat count and distance methods.
LA - eng
KW - Poisson point process; asymptotically uniform distributions; weak convergence; variation distance; rate of convergence; Poisson hypothesis testing; distance method; quadrat count method; oscillating point patterns; isotropic Gaussian oscillations; oscillating point patterns; weak convergence; rate of convergence; quadrat count method; isotropic Gaussian oscillations; Poisson point process
UR - http://eudml.org/doc/15748
ER -