Central limit theorem for random measures generated by stationary processes of compact sets

Zbyněk Pawlas

Kybernetika (2003)

  • Volume: 39, Issue: 6, page [719]-729
  • ISSN: 0023-5954

Abstract

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Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.

How to cite

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Pawlas, Zbyněk. "Central limit theorem for random measures generated by stationary processes of compact sets." Kybernetika 39.6 (2003): [719]-729. <http://eudml.org/doc/33676>.

@article{Pawlas2003,
abstract = {Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.},
author = {Pawlas, Zbyněk},
journal = {Kybernetika},
keywords = {central limit theorem; fibre process; point process; random measure; space of compact sets; central limit theorem; fibre process; point process; random measure; space of compact sets},
language = {eng},
number = {6},
pages = {[719]-729},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Central limit theorem for random measures generated by stationary processes of compact sets},
url = {http://eudml.org/doc/33676},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Pawlas, Zbyněk
TI - Central limit theorem for random measures generated by stationary processes of compact sets
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 6
SP - [719]
EP - 729
AB - Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.
LA - eng
KW - central limit theorem; fibre process; point process; random measure; space of compact sets; central limit theorem; fibre process; point process; random measure; space of compact sets
UR - http://eudml.org/doc/33676
ER -

References

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  7. Heinrich L., Schmidt V., 10.2307/1427084, Adv. in Appl. Probab. 17 (1985), 709–730 (1985) Zbl0609.60036MR0809427DOI10.2307/1427084
  8. Pawlas Z., Beneš V., On the central limit theorem for the stationary Poisson process of compact sets, Math. Nachr. (2003), to appear MR2047386
  9. Robbins H., 10.1090/S0002-9904-1948-09142-X, Bull. Amer. Math. Soc. 54 (1948), 1151–1161 (1948) Zbl0034.22503MR0027974DOI10.1090/S0002-9904-1948-09142-X
  10. Stoyan D., Kendall W. S., Mecke J., Stochastic Geometry and Its Applications, Second edition. Wiley, New York, 1995 Zbl1155.60001MR0895588

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