Empirical distributions in marked point processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Pawlas, Zbynek^1,2 

[1] Charles Univ Prague, Fac Math & Phys, Dept Probabil & Math Stat, Prague 18675, Czech Republic

[2] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark

关键词: Empirical process;    Geostatistical marking;    Germ-grain process;    Marked point process;    Random fields;    Strong mixing;   

DOI  :  10.1016/j.spa.2009.10.002

来源: Elsevier

【 摘 要 】

We study the asymptotic behaviour of the empirical distribution function derived from a stationary marked point process when a convex sampling window is expanding without bounds in all directions. We consider a random field model which assumes that the marks and the points are independent and admits dependencies between the marks. The main result is the weak convergence of the empirical process under strong mixing conditions on both independent components of the model. Applying an approximation principle weak convergence can be also shown for appropriately weighted empirical process defined from a stationary d-dimensional germ-grain process with dependent grains. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free