Abstract
A proof of the Rosenthal inequality for α-mixing random fields is given. The statements and proofs are modifications of the corresponding results obtained by Doukhan and Utev.
Similar content being viewed by others
References
I. Fazekas and A. G. Kukush, “Asymptotic properties of an estimator in nonlinear functional errors-in-variables models with dependent error terms”, Comput. Math. Appl., 34, No. 10, 23–39 (1997).
H. P. Rosenthal, “On the subspaces of L p (p > 2) spanned by sequences of independent random variables”, Isr. J. Math., 8, 273–303 (1970).
S. A. Utev, “Inequalities for sums of weakly dependent random variables and rate of convergence in invariance principle,” in: Limit Theorems for Sums of Random Variables [in Russian], Nauka, Novosibirsk (1984), pp. 50–70.
P. Doukhan, Mixing. Properties and Example, Springer, New York 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fazekas, I., Kukush, A.G. & Tómács, T. On the rosenthal inequality for mixing fields. Ukr Math J 52, 305–318 (2000). https://doi.org/10.1007/BF02529642
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02529642