Previous |  Up |  Next

Article

Title: Central limit theorem for random measures generated by stationary processes of compact sets (English)
Author: Pawlas, Zbyněk
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 39
Issue: 6
Year: 2003
Pages: [719]-729
Summary lang: English
.
Category: math
.
Summary: 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. (English)
Keyword: central limit theorem
Keyword: fibre process
Keyword: point process
Keyword: random measure
Keyword: space of compact sets
MSC: 60D05
MSC: 60F05
MSC: 60G57
idZBL: Zbl 1249.60015
idMR: MR2035646
.
Date available: 2009-09-24T19:58:15Z
Last updated: 2015-03-24
Stable URL: http://hdl.handle.net/10338.dmlcz/135567
.
Reference: [1] Daley D. J., Vere-Jones D.: An Introduction to the Theory of Point Processes.Springer–Verlag, New York 1988 Zbl 1159.60003, MR 0950166
Reference: [2] Fritz J.: Generalization of McMillan’s theorem to random set functions.Studia Sci. Math. Hungar. 5 (1970), 369–394 MR 0293956
Reference: [3] Gnedenko B. V., Korolev V. Y.: Random Summation: Limit Theorems and Applications.CRC Press, Boca Raton 1996 Zbl 0857.60002, MR 1387113
Reference: [4] Grandell J.: Doubly Stochastic Poisson Processes.(Lecture Notes in Mathematics 529.) Springer–Verlag, Berlin 1976 Zbl 0339.60053, MR 0433591
Reference: [5] Heinrich L.: Normal approximation for some mean-value estimates of absolutely regular tessellations.Math. Methods Statist. 3 (1994), 1–24 Zbl 0824.60011, MR 1272628
Reference: [6] Heinrich L., Molchanov I. S.: Central limit theorem for a class of random measures associated with germ-grain models.Adv. in Appl. Probab. 31 (1999), 283–314 Zbl 0941.60025, MR 1724553, 10.1239/aap/1029955136
Reference: [7] Heinrich L., Schmidt V.: Normal convergence of multidimensional shot noise and rates of this convergence.Adv. in Appl. Probab. 17 (1985), 709–730 Zbl 0609.60036, MR 0809427, 10.2307/1427084
Reference: [8] Pawlas Z., Beneš V.: On the central limit theorem for the stationary Poisson process of compact sets.Math. Nachr. (2003), to appear MR 2047386
Reference: [9] Robbins H.: The asymptotic distribution of the sum of a random number of random variables.Bull. Amer. Math. Soc. 54 (1948), 1151–1161 Zbl 0034.22503, MR 0027974, 10.1090/S0002-9904-1948-09142-X
Reference: [10] Stoyan D., Kendall W. S., Mecke J.: Stochastic Geometry and Its Applications.Second edition. Wiley, New York, 1995 Zbl 1155.60001, MR 0895588
.

Files

Files Size Format View
Kybernetika_39-2003-6_4.pdf 1.137Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo