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.
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.
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@article{CRMATH_2002__334_8_705_0, author = {Maumy, Myriam}, 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}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02293-8/} }
TY - JOUR AU - Maumy, Myriam 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 UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02293-8/ DO - 10.1016/S1631-073X(02)02293-8 LA - fr ID - CRMATH_2002__334_8_705_0 ER -
Maumy, Myriam. Sur les oscillations du processus de Poisson composé. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 705-708. doi : 10.1016/S1631-073X(02)02293-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02293-8/
[1] Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc., Volume 57 (1962), pp. 33-45
[2] Nonstandard strong laws for local quantile processes, J. Statist. Planning Inference, Volume 91 (2000), pp. 239-266
[3] Some properties of weighted compound multivariate empirical processes, Indian J. Statist., Volume 48 (1986), pp. 393-403
[4] An empirical process approach to the uniform consistency of kernel-type function estimators, J. Theoret. Probab., Volume 13 (2000), pp. 1-37
[5] A rank statistics approach to the consistency of a general bootstrap, Ann. Statist., Volume 20 (1992), pp. 1611-1624
[6] Stochastic Processes, Holden-Day, 1962
[7] Empirical Processes with Applications to Statistics, Wiley, 1986
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