Bernoulli

  • Bernoulli
  • Volume 12, Number 3 (2006), 501-514.

Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality

Michael V. Boutsikas

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Abstract

We present a general and quite simple upper bound for the total variation distance d TV between any stochastic process ( X i ) i Γ defined over a countable space Γ , and a compound Poisson process on Γ . This result is sufficient for proving weak convergence for any functional of the process ( X i ) i Γ when the real-valued X i 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.

Article information

Source
Bernoulli, Volume 12, Number 3 (2006), 501-514.

Dates
First available in Project Euclid: 28 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1151525133

Digital Object Identifier
doi:10.3150/bj/1151525133

Mathematical Reviews number (MathSciNet)
MR2232729

Zentralblatt MATH identifier
1114.60022

Keywords
compound Poisson process approximation coupling inequality law of small numbers locally dependent variables moving sums rate of convergence success runs total variation distance

Citation

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


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