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On the rate of Poisson approximation to Bernoulli partial sum processes

Author

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  • Ruzankin, Pavel S.
  • Borisov, Igor S.

Abstract

We investigate approximation of a Bernoulli partial sum process to the accompanying Poisson process in the non-i.i.d. case. The rate of closeness is studied in terms of the minimal distance in probability. In particular, a new lower bound for the total variation distance between a Bernoulli partial sum process and the accompanying Poisson process is obtained.

Suggested Citation

  • Ruzankin, Pavel S. & Borisov, Igor S., 2020. "On the rate of Poisson approximation to Bernoulli partial sum processes," Statistics & Probability Letters, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:stapro:v:162:y:2020:i:c:s0167715220300572
    DOI: 10.1016/j.spl.2020.108754
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    References listed on IDEAS

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    1. Borisov, I. S., 2000. "A note on Poisson approximation of rescaled set-indexed empirical processes," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 101-103, January.
    2. Adell, JoséA. & de la Cal, Jesús, 1996. "Optimal Poisson approximation of uniform empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 135-142, November.
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