- Volume 12, Number 3 (2006), 501-514.
Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality
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.
Bernoulli, Volume 12, Number 3 (2006), 501-514.
First available in Project Euclid: 28 June 2006
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Boutsikas, Michael V. Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality. Bernoulli 12 (2006), no. 3, 501--514. doi:10.3150/bj/1151525133. https://projecteuclid.org/euclid.bj/1151525133