Geodesic
Exponential tightness for integral -- type functionals of centered independent differently distributed random variables
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 273-284.

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Exponential tightness is proved for a sequence of integral – type random fields constructed by centered independent differently distributed random variables. This result is proven using sufficient conditions for the exponential tightness of a sequence of continuous random fields of arbitrary form, which are also obtained in this paper.
Keywords: random field, large deviations principle, moderate deviations principle, exponential tightness.
Mots-clés : Cramer's moment condition 
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A. V. Logachov; A. A. Mogulskii. Exponential tightness for integral -- type functionals of centered independent differently distributed random variables. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 273-284. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a17/

[1] A.A. Pukhal'skij, “On the theory of large deviations”, Theory probab. Appl., 38:3 (1993), 490–497 | DOI | MR | Zbl

[2] A. Dembo, O. Zeitouni, Large deviations techniques and applications, Applications of Mathematics, 38, Springer, New York, 1998 | MR | Zbl

[3] A.V. Logachov, A.A. Mogul'skii, “Exponential Chebyshev inequalities for random graphons and their applications”, Sib. Math. J., 61:4 (2020), 697–714 | DOI | MR | Zbl

[4] S. Chatterjee, Large deviations for random graphs, Lecture Notes in Mathematics, 2197, Springer, Cham, 2017 | DOI | MR | Zbl

[5] J.L. Kelley, General topology, Graduate Texts in Mathematics, 27, Springer, New York, etc., 1975 | MR | Zbl

[6] A.A. Pukhal'skij, “On functional principle of large deviations”, New trends in probability and statistics, Proc. 23rd Bakuriani Colloq. in Honour of Yu. V. Prokhorov (Bakuriani/USSR 1990), v. 1, eds. V.V. Sazonov, T. L. Shervashidze, De Gruyter, Berlin–Boston, 1991, 198–219 | MR | Zbl

[7] J. Feng, T. Kurtz, Large deviations for stochastic processes, Mathematical Surveys and Monographs, 131, AMS, Providence, 2006 | DOI | MR | Zbl

[8] E. Ostrovsky, L. Sirota, Sufficient conditions for exponential tightness of normed sums of independent random fields in the space of continuous function, 2014, arXiv: 1403.7562