Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2023_20_2_a28, author = {E. V. Efremov and A. V. Logachov}, title = {On the moderate deviation principle for $m$-dependent random variables with sublinear expectation}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {961--980}, publisher = {mathdoc}, volume = {20}, number = {2}, year = {2023}, language = {en}, url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a28/} }
TY - JOUR AU - E. V. Efremov AU - A. V. Logachov TI - On the moderate deviation principle for $m$-dependent random variables with sublinear expectation JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2023 SP - 961 EP - 980 VL - 20 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a28/ LA - en ID - SEMR_2023_20_2_a28 ER -
%0 Journal Article %A E. V. Efremov %A A. V. Logachov %T On the moderate deviation principle for $m$-dependent random variables with sublinear expectation %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2023 %P 961-980 %V 20 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a28/ %G en %F SEMR_2023_20_2_a28
E. V. Efremov; A. V. Logachov. On the moderate deviation principle for $m$-dependent random variables with sublinear expectation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 961-980. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a28/
[1] A.A. Borovkov, Asymptotic analysis of random walks: light-tailed distributions, Cambridge University Press, Cambridge, 2020 | MR | Zbl
[2] A.A. Borovkov, A.A. Mogulskii, “Moderately large deviation principles for the trajectories of random walks and processes with independent increments”, Theory Probab. Appl., 58:4 (2014), 562–581 | DOI | MR | Zbl
[3] A.A. Lebedev, V.A. Lebedev, “Generalization of the expectation for a unified description of random and indefinite factors”, Theory Probab. Appl., 38:3 (1993), 470–478 | DOI | MR | Zbl
[4] J.-D. Deuschel, D.W. Stroock, Large deviations, Academic Press, Boston etc, 1989 | MR | Zbl
[5] A. Dembo, O. Zeitouni, Large deviations techniques and applications, 2nd ed., Springer, New York, 1998 | MR | Zbl
[6] S. Peng, Nonlinear expectations and stochastic calculus under uncertainty, Springer, Berlin, 2019 | MR | Zbl
[7] S. Peng, “G-expectation, G-Brownian motion and related stochastic calculus of Itô type”, Stochastic analysis and applications, The Abel symposium 2005, Proceedings of the second Abel symposium, eds. Benth Fred Espen et al., Springer, Berlin, 2007, 541–567 | DOI | MR | Zbl
[8] S. Peng, “Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation”, Stoch. Process. Appl., 118:12 (2008), 2223–2253 | DOI | MR | Zbl
[9] S. Peng, “Law of large numbers and central limit theorem under nonlinear expectations”, Probab. Uncertain. Quant. Risk, 4 (2019), 4 | DOI | MR | Zbl
[10] Z. Chen, P. Wu, B. Li, “A strong law of large numbers for non-additive probabilities”, Int. J. Approx. Reasoning, 54:3 (2013), 365–377 | DOI | MR | Zbl
[11] W. Liu, Y. Zhang, “Large deviation principle for linear processes generated by real stationary sequences under the sub-linear expectation”, Commun. Stat., Theory Methods, 52:16 (2023), 5727–5741 | DOI | MR | Zbl
[12] F. Hu, “On Cramér's theorem for capacities”, C. R., Math., Acad. Sci. Paris, 348:17-18 (2010), 1009–1013 | MR | Zbl
[13] F. Gao, M. Xu, “Large deviations and moderate deviations for independent random variables under sublinear expectations”, Sci. Sin., Math., 41:4 (2011), 337–352 | DOI | MR | Zbl
[14] X. Cao, “An upper bound of large deviations for capacities”, Math. Probl. Eng., 2014, 516291 | MR | Zbl
[15] Z. Chen, X. Feng, “Large deviation for negatively dependent random variables under sublinear expectation”, Commun. Stat., Theory Methods, 45:2 (2016), 400–412 | DOI | MR | Zbl
[16] Y. Tan, G. Zong, “Large deviation principle for random variables under sublinear expectations on $\mathbb{R}^d$”, J. Math. Anal. Appl., 488:2 (2020), 124110 | DOI | MR | Zbl
[17] Z. Chen, J. Xiong, “Large deviation principle for diffusion processes under a sublinear expectation”, Sci. China Math., 55:11 (2012), 2205–2216 | DOI | MR | Zbl
[18] F. Gao, H. Jiang, “Large deviations for stochastic differential equations driven by G-Brownian motion”, Stochastic Processes Appl., 120:11 (2010), 2212–2240 | DOI | MR | Zbl
[19] Q.Q. Zhou, A.V. Logachov, “Moderate deviations principle for independent random variables under sublinear expectations”, Sib. Èlektron. Math. Izv., 18:2 (2021), 817–826 | DOI | MR | Zbl
[20] S. Guo, Z. Yong, “Moderate deviation principle for m-dependent random variables under the sublinear expectation”, AIMS Mathematics, 7:4 (2022), 5943–5956 | DOI | MR