Comptes Rendus
Sur les oscillations du processus de Poisson composé
[On the oscillations of compound empirical processes]
Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 705-708.

In this paper, we describe the local behaviour of compound Poisson processes based on a Poisson process and a sequence of independent and identically distributed random weights. These results are motived by their natural counterparts in the theory of empirical processes.

Dans cette Note, nous établissons des lois limites décrivant le comportement local du processus de Poisson composé construit à partir d'un processus de Poisson et d'une suite de variables aléatoires indépendantes et identiquement distribuées. Ces résultats sont motivés par leurs applications naturelles à la théorie des processus empiriques.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02293-8

Myriam Maumy 1

1 LSTA, Université Paris VI, boı̂te Courrier 158, 8
@article{CRMATH_2002__334_8_705_0,
     author = {Myriam Maumy},
     title = {Sur les oscillations du processus de {Poisson} compos\'e},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {705--708},
     publisher = {Elsevier},
     volume = {334},
     number = {8},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02293-8},
     language = {fr},
}
TY  - JOUR
AU  - Myriam Maumy
TI  - Sur les oscillations du processus de Poisson composé
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 705
EP  - 708
VL  - 334
IS  - 8
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02293-8
LA  - fr
ID  - CRMATH_2002__334_8_705_0
ER  - 
%0 Journal Article
%A Myriam Maumy
%T Sur les oscillations du processus de Poisson composé
%J Comptes Rendus. Mathématique
%D 2002
%P 705-708
%V 334
%N 8
%I Elsevier
%R 10.1016/S1631-073X(02)02293-8
%G fr
%F CRMATH_2002__334_8_705_0
Myriam Maumy. Sur les oscillations du processus de Poisson composé. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 705-708. doi : 10.1016/S1631-073X(02)02293-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02293-8/

[1] G. Bennett Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc., Volume 57 (1962), pp. 33-45

[2] P. Deheuvels Nonstandard strong laws for local quantile processes, J. Statist. Planning Inference, Volume 91 (2000), pp. 239-266

[3] J.H.J. Einmahl; F.H. Ruymgaart Some properties of weighted compound multivariate empirical processes, Indian J. Statist., Volume 48 (1986), pp. 393-403

[4] U. Einmahl; D.M. Mason An empirical process approach to the uniform consistency of kernel-type function estimators, J. Theoret. Probab., Volume 13 (2000), pp. 1-37

[5] D.M. Mason; M.A. Newton A rank statistics approach to the consistency of a general bootstrap, Ann. Statist., Volume 20 (1992), pp. 1611-1624

[6] E. Parzen Stochastic Processes, Holden-Day, 1962

[7] G.R. Shorack; J.A. Wellner Empirical Processes with Applications to Statistics, Wiley, 1986

Cited by Sources:

Comments - Policy