Bernoulli

  • Bernoulli
  • Volume 17, Number 4 (2011), 1268-1284.

Absolute regularity and ergodicity of Poisson count processes

Michael H. Neumann

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Abstract

We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that a stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables, we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.

Article information

Source
Bernoulli, Volume 17, Number 4 (2011), 1268-1284.

Dates
First available in Project Euclid: 4 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1320417504

Digital Object Identifier
doi:10.3150/10-BEJ313

Mathematical Reviews number (MathSciNet)
MR2854772

Zentralblatt MATH identifier
1277.60089

Keywords
absolute regularity ergodicity integer-valued process mixing Poisson count process test

Citation

Neumann, Michael H. Absolute regularity and ergodicity of Poisson count processes. Bernoulli 17 (2011), no. 4, 1268--1284. doi:10.3150/10-BEJ313. https://projecteuclid.org/euclid.bj/1320417504


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