Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality
Michael V. Boutsikas
Source: Bernoulli Volume 12, Number 3
(2006), 501-514.
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.
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Keywords: compound Poisson process approximation; coupling inequality; law of small numbers; locally dependent variables; moving sums; rate of convergence; success runs; total variation distance
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1151525133
Digital Object Identifier: doi:10.3150/bj/1151525133
Mathematical Reviews number (MathSciNet): MR2232729
Zentralblatt MATH identifier: 1114.60022
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