Generalization of the law of the iterated logarithm for associated random fields

详细信息    查看全文

• 作者：A. P. Shashkin
• 关键词：law of the iterated logarithm ; associated randomfield ; indexing set ; multi ; indexed random variable ; covariance function ; Cox–Grimmet coefficients ; Bolthausen theorem
• 刊名：Mathematical Notes
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：98
• 期：5-6
• 页码：831-842
• 全文大小：721 KB
• 参考文献：1.A. V. Bulinskii, “A new variant of the functional law of the iterated logarithm,” Teor. Veroyatnost. Primenen. 25 (3), 502–512 (1980) [Theory Probab. Appl. 25 (3), 493–503 (1981)].MathSciNet
  2.Y.-C. Qi, “On strong convergence of arrays,” Bull. Austral. Math. Soc. 50 (2), 219–223 (1994).MATH MathSciNet CrossRef
  3.A. V. Bulinskii and M. A. Lifshits, “Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors,” Uspekhi Mat. Nauk 50 (5), 83–102 (1995) [Russian Math. Surveys 50 (5), 925–944 (1995)].MathSciNet
  4.G. J. Zimmerman, “Some sample function properties of the two-parameter Gaussian process,” Ann. Math. Statist. 43, 1235–1246 (1972).MATH MathSciNet CrossRef
  5.M. J. Wichura, “Some Strassen-type laws of the iterated logarithm for multiparameter stochastic processes with independent increments,” Ann. Probab. 1, 272–296 (1973).MATH MathSciNet CrossRef
  6.M. T. Lacey, “A remark on the multiparameter law of the iterated logarithm,” Stochastic Process. Appl. 32 (2), 355–367 (1989).MATH MathSciNet CrossRef
  7.A. Gut, F. Johnson and U. StadtmÜller, “Between the LIL and the LSL,” Bernoulli 16 (1), 1–22 (2010).MATH MathSciNet CrossRef
  8.A. Shashkin, “A variant of the LIL for multiparameter Brownian motion,” in Transactions of XXV International Seminar on Stability Problems for Stochastic Models, Maiori (Salerno), Italy, September 20–24 (Maiori, 2005), pp. 258–263.
  9.A. V. Bulinskii and A. P. Shashkin, Limit Theorems for Associated Random Fields and Related Systems (Fizmatlit, Moscow, 2008) [in Russian].
  10.A. V. Bulinskii, “The functional law of the iterated logarithm for associated random fields,” Fundam. Prikl. Mat. 1 (3), 623–639 (1995).MathSciNet
  
• 作者单位：A. P. Shashkin (1)
  
  1. Lomonosov Moscow State University, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

A variant of the law of the iterated logarithm for associated fields for which the indexing set for partial sums can be arbitrarily unbounded is proved. Depending on the structure of this set, an explicit value of the upper limit in the law of the iterated logarithm is given. Keywords law of the iterated logarithm associated randomfield indexing set multi-indexed random variable covariance function Cox–Grimmet coefficients Bolthausen theorem