Poisson perturbations

Andrew D. Barbour; Aihua Xia

ESAIM: Probability and Statistics (1999)

  • Volume: 3, page 131-150
  • ISSN: 1292-8100

How to cite

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Barbour, Andrew D., and Xia, Aihua. "Poisson perturbations." ESAIM: Probability and Statistics 3 (1999): 131-150. <http://eudml.org/doc/104253>.

@article{Barbour1999,
author = {Barbour, Andrew D., Xia, Aihua},
journal = {ESAIM: Probability and Statistics},
keywords = {Stein's method; signed compound Poisson measure; total variation; coupling; sums of random variables; compound measures},
language = {eng},
pages = {131-150},
publisher = {EDP Sciences},
title = {Poisson perturbations},
url = {http://eudml.org/doc/104253},
volume = {3},
year = {1999},
}

TY - JOUR
AU - Barbour, Andrew D.
AU - Xia, Aihua
TI - Poisson perturbations
JO - ESAIM: Probability and Statistics
PY - 1999
PB - EDP Sciences
VL - 3
SP - 131
EP - 150
LA - eng
KW - Stein's method; signed compound Poisson measure; total variation; coupling; sums of random variables; compound measures
UR - http://eudml.org/doc/104253
ER -

References

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  1. [1] M. Abramowitz and I.A. Stegun, Handbook of mathematical functions. Dover, New York ( 1964). 
  2. [2] R. Arratia, A.D. Barbour and S. Tavaré, The number of components in a logarithmic combinatorial structure. Ann. Appl. Probab., to appear. Zbl1056.60012MR1768242
  3. [3] R. Arratia, L. Goldstein and L. Gordon, Poisson approximation and the Chen-Stein method. Stat. Science 5 ( 1990) 403-434. Zbl0955.62542MR1092983
  4. [4] A.D. Barbour and J.L. Jensen, Local and tail approximations near the Poisson limit. Scand. J. Statist. 16 ( 1989) 75-87. Zbl0674.60022MR1003970
  5. [5] A.D. Barbour and S. Utev, Solving the Stein equation in compound Poisson approximationAdv. in Appl. Probab. 30 ( 1998) 449-475. Zbl0982.62007MR1642848
  6. [6] A.D. Barbour and S. Utev, Compound Poisson approximation in total variation. Stochastic Process. Appl., to appear. Zbl0991.62008MR1695071
  7. [7] V. Čekanavičius, Asymptotic expansions in the exponent: A compound Poisson approach. Adv. in Appl. Probab. 29 ( 1997) 374-387. Zbl0895.60029MR1450935
  8. [8] P. Eichelsbacher and M. Roos, Compound Poisson approximation for dissociated random variables via Stein's method ( 1998) preprint. Zbl0982.62008MR1723647
  9. [9] J. Kruopis, Precision of approximations of the generalized Binomial distribution by convolutions of Poisson measures. Lithuanian Math. J. 26 ( 1986) 37-49. Zbl0631.60019
  10. [10] T. Lindvall, Lectures on the coupling method. Wiley, New York ( 1992). Zbl0850.60019MR1180522
  11. [11] E.L. Presman, Approximation of binomial distributions by infinitely divisible ones. Theory. Probab. Appl. 28 ( 1983) 393-403. Zbl0533.60018MR700218
  12. [12] D.A. Raikov, On the decomposition of Gauss and Poisson laws. Izv. Akad. Nauk Armyan. SSR Ser. Mat. 2 ( 1938) 91-124. Zbl0018.41204
  13. [13] M. Roos, Stein-Chen method for compound Poisson approximation. Ph. D. Dissertation, University of Zürich ( 1993). Zbl0853.60020

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