Functional Central Limit Theorem for Excursion set Volumes of Quasi-Associated Random Fields

被引：0
作者：
Demichev V.P. [1 ]
机构：
[1] Moscow State University, Moscow
来源：
Journal of Mathematical Sciences | 2015年 / 204卷 / 1期
关键词：
Random Field; Central Limit Theorem; Functional Version; Lipschitz Continuous Function; Functional Central Limit Theorem;
D O I：
10.1007/s10958-014-2187-2
中图分类号：
学科分类号：
摘要：
Stationary quasi-associated random fields with continuous covariance function are considered. Recently, Bulinski, Spodarev, and Timmermann proved a central limit theorem for the excursion set volumes of such random fields. We establish a functional version of this theorem. Bibliography: 11 titles. © 2014, Springer Science+Business Media New York.
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页码：69 / 77
页数：8
相关论文
共 11 条
  • [1] Adler R.J., Taylor J.E., Random Fields and Geometry, (2007)
  • [2] Azais J.-M., Wschebor M., Level Sets and Extrema of Random Processes and Fields, (2009)
  • [3] Leonenko N.N., Ivanov A.V., Statistical Analysis of Random Fields [in Russian], Kiev, (1986)
  • [4] Bulinski A.V., Spodarev E., Timmermann F., Central limit theorems for the excursion set volumes of weakly dependent random fields, Bernoulli, 18, pp. 100-118, (2012)
  • [5] Meschenmoser D., Shashkin A., Functional central limit theorem for the volume of excursion sets generated by associated random fields, Statist. Probab. Lett., 81, pp. 642-646, (2011)
  • [6] Bulinski A.V., Suquet C., Normal approximation for quasi-associated random fields, Statist. Probab. Lett., 54, pp. 215-226, (2001)
  • [7] Bulinskii A.V., Shabanovich E., Asymptotic behavior of some functionals of positively and negatively dependent random fields, Fundam. Prikl. Mat., 4, pp. 479-492, (1998)
  • [8] Shashkin A.P., Quasi-associatedness of a Gaussian system of random vectors, Usp. Mat. Nauk., 57, pp. 199-200, (2002)
  • [9] Shao Q.-M., Yu H., Weak convergence for weighted empirical processes of dependent sequences,, Ann. Probab., 24, pp. 2098-2127, (1996)
  • [10] Bulinskii A.V., Shashkin A.P., Limit Theorems for Associated Random Fields and Related Systems [in Russian], Moscow, (2008)
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