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On the rosenthal inequality for mixing fields

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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.

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References

  1. 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).

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  3. 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.

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  4. P. Doukhan, Mixing. Properties and Example, Springer, New York 1994.

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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

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  • DOI: https://doi.org/10.1007/BF02529642

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