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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 1998, Volume 4, Issue 2, Pages 479–492 (Mi fpm305)

Asymptotical behaviour for some functionals of positively and negatively dependent random fields

A. V. Bulinskia, E. Shabanovichb

a M. V. Lomonosov Moscow State University
b University of Montenegro

Abstract: Using Stein–Goetze–Barbour techniques we estimate the proximity of values of a functional of certain class taken respectively on processes of weighted partial sums type and on appropriate Gaussian processes. The former processes arise from random fields on $\mathbb Z^d$ which are either weakly associated or negatively dependent.

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Bibliographic databases:
UDC: 519.21

Citation: A. V. Bulinski, E. Shabanovich, “Asymptotical behaviour for some functionals of positively and negatively dependent random fields”, Fundam. Prikl. Mat., 4:2 (1998), 479–492

Citation in format AMSBIB
\Bibitem{BulSha98}
\by A.~V.~Bulinski, E.~Shabanovich
\paper Asymptotical behaviour for some functionals of positively and negatively dependent random fields
\jour Fundam. Prikl. Mat.
\yr 1998
\vol 4
\issue 2
\pages 479--492
\mathnet{http://mi.mathnet.ru/fpm305}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1801168}
\zmath{https://zbmath.org/?q=an:0968.60044}

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. A. Vronskii, “Refinement of the almost sure central limit theorem for associated processes”, Math. Notes, 68:4 (2000), 444–451
2. Bulinski, A, “Normal approximation for quasi-associated random fields”, Statistics & Probability Letters, 54:2 (2001), 215
3. A. P. Shashkin, “Maximal Inequality for Weakly Dependent Random Fields”, Math. Notes, 75:5 (2004), 717–725
4. A. V. Bulinski, “Statistical Version of the Central Limit Theorem for Vector-Valued Random Fields”, Math. Notes, 76:4 (2004), 455–464
5. Bulinski, AV, “Strong invariance principle for dependent multi-indexed random variables”, Doklady Mathematics, 72:1 (2005), 503
6. A. P. Shashkin, “The law of the iterated logarithm for an associated random field”, Russian Math. Surveys, 61:2 (2006), 359–361
7. N. Yu. Kryzhanovskaya, “Moment Inequality for Sums of Multi-Indexed Dependent Random Variables”, Math. Notes, 83:6 (2008), 770–782
8. Shashkin, A, “A strong invariance principle for positively or negatively associated random fields”, Statistics & Probability Letters, 78:14 (2008), 2121
9. Bulinski A., “Central Limit Theorem for Random Fields and Applications”, Advances in Data Analysis - Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks, Statistics for Industry and Technology, 2010, 141–150
10. Shashkin A., “A Berry-Esseen Type Estimate for Dependent Systems on Transitive Graphs”, Advances in Data Analysis - Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks, Statistics for Industry and Technology, 2010, 151–156
11. Bulinski A., Spodarev E., Timmermann F., “Central limit theorems for the excursion set volumes of weakly dependent random fields”, Bernoulli, 18:1 (2012), 100–118
12. V. P. Demichev, “Functional central limit theorem for excursion set volumes of quasi-associated random fields”, J. Math. Sci. (N. Y.), 204:1 (2015), 69–77
13. V. P. Demichev, “A Central Limit Theorem for Integrals with Respect to Random Measures”, Math. Notes, 95:2 (2014), 193–203
14. Hadjila T., Ahmed A.S., “Estimation and Simulation of Conditional Hazard Function in the Quasi-Associated Framework When the Observations Are Linked Via a Functional Single-Index Structure”, Commun. Stat.-Theory Methods, 47:4 (2018), 816–838
15. Poinas A., Delyon B., Lavancier F., “Mixing Properties and Central Limit Theorem For Associated Point Processes”, Bernoulli, 25:3 (2019), 1724–1754
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