We present a general and quite simple upper bound for the total variation distance [math] between any stochastic process [math] defined over a countable space [math] , and a compound Poisson process on [math] This result is sufficient for proving weak convergence for any functional of the process [math] when the real-valued [math] are rarely non-zero and locally dependent. Our result is established after introducing and employing a generalization of the basic coupling inequality. Finally, two simple examples of application are presented in order to illustrate the applicability of our results.
Publié le : 2006-06-14
Classification:
compound Poisson process approximation,
coupling inequality,
law of small numbers,
locally dependent variables,
moving sums,
rate of convergence,
success runs,
total variation distance
@article{1151525133,
author = {Boutsikas, Michael V.},
title = {Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality},
journal = {Bernoulli},
volume = {12},
number = {2},
year = {2006},
pages = { 501-514},
language = {en},
url = {http://dml.mathdoc.fr/item/1151525133}
}
Boutsikas, Michael V. Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality. Bernoulli, Tome 12 (2006) no. 2, pp. 501-514. http://gdmltest.u-ga.fr/item/1151525133/