Absolute continuity and local limit theorems for homogeneous functionals of point processes

被引：0
|
作者：
Davydov, Youri [1 ,2 ]
Kaim, Michael [3 ]
机构：
[1] St Petersburg State Univ, Line 14,29A VO, St Petersburg 199178, Russia
[2] Univ Lille, Lab Paul Painleve, Cite Sci, F-59655 Villeneuve Dascq, France
[3] Lycee Montebello, 196 Blvd Montebello, F-59000 Lille, France
来源：
LITHUANIAN MATHEMATICAL JOURNAL | 2019年 / 59卷 / 04期
关键词：
absolute continuity; empirical point processes; local limit theorems; convergence in total variation;
D O I：
10.1007/s10986-019-09460-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the absolute continuity and local limit theorems for homogeneous functionals defined on configurations of point processes (p.p.s). For empirical p.p.s, we show that under mild hypotheses the distribution of such a functional has a density. Moreover, we present results on convergence in total variation of this distribution to some limit.
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页码：498 / 506
页数：9
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