Abstract
We present a general and quite simple upper bound for the total variation distance between any stochastic process defined over a countable space , and a compound Poisson process on This result is sufficient for proving weak convergence for any functional of the process when the real-valued 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.
Citation
Michael V. Boutsikas. "Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality." Bernoulli 12 (3) 501 - 514, June 2006. https://doi.org/10.3150/bj/1151525133
Information