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.

引用

页码：498 / 506

页数：9

共 50 条

[1] Absolute continuity and local limit theorems for homogeneous functionals of point processes
Youri Davydov
Michaël Kaim
Lithuanian Mathematical Journal, 2019, 59 : 498 - 506
[2] LIMIT-THEOREMS FOR POINT-PROCESSES AND THEIR FUNCTIONALS
KASAHARA, Y
WATANABE, S
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1986, 38 (03) : 543 - 574
[3] Limit theorems for geometric functionals of Gibbs point processes
Schreiber, T.
Yukich, J. E.
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2013, 49 (04): : 1158 - 1182
[4] LOCAL LIMIT-THEOREMS FOR FUNCTIONALS OF RANDOM-PROCESSES
DAVYDOV, YA
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1988, 33 (04) : 732 - 738
[5] LOCAL LIMIT-THEOREMS FOR FUNCTIONALS OF GAUSSIAN-PROCESSES
DAVYDOV, YA
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1982, 26 (04) : 856 - 857
[6] ABSOLUTE CONTINUITY OF DISTRIBUTIONS OF FUNCTIONALS OF RANDOM PROCESSES
DAVYDOV, YA
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1978, 23 (01) : 218 - 219
[7] LIMIT THEOREMS FOR FUNCTIONALS OF MEASURABLE RANDOM PROCESSES
GRINBLAT, LS
DOKLADY AKADEMII NAUK SSSR, 1968, 181 (02): : 275 - &
[8] LIMIT THEOREMS FOR EMPIRICAL PROCESSES OF CLUSTER FUNCTIONALS
Drees, Holger
Rootzen, Holger
ANNALS OF STATISTICS, 2010, 38 (04): : 2145 - 2186
[9] LIMIT THEOREMS FOR HOMOGENEOUS STOCHASTIC PROCESSES
BOCHNER, S
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1954, 40 (08) : 699 - 703
[10] THE ABSOLUTE CONTINUITY OF DISTRIBUTIONS OF FUNCTIONALS OF DIFFUSION-PROCESSES
SMORODINA, NV
RUSSIAN MATHEMATICAL SURVEYS, 1982, 37 (06) : 205 - 213

← 1 2 3 4 5 →