Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2021_18_2_a18, author = {Q. Q. Zhou and A. V. Logachov}, title = {Moderate deviations principle for independent random variables under sublinear expectations}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {817--826}, publisher = {mathdoc}, volume = {18}, number = {2}, year = {2021}, language = {en}, url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a18/} }
TY - JOUR AU - Q. Q. Zhou AU - A. V. Logachov TI - Moderate deviations principle for independent random variables under sublinear expectations JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2021 SP - 817 EP - 826 VL - 18 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a18/ LA - en ID - SEMR_2021_18_2_a18 ER -
%0 Journal Article %A Q. Q. Zhou %A A. V. Logachov %T Moderate deviations principle for independent random variables under sublinear expectations %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2021 %P 817-826 %V 18 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a18/ %G en %F SEMR_2021_18_2_a18
Q. Q. Zhou; A. V. Logachov. Moderate deviations principle for independent random variables under sublinear expectations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 817-826. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a18/
[1] X. Cao, “An upper bound of large deviations for capacities”, Math. Probl. Eng., 2014:2014, 516291 | Zbl
[2] Z. Chen, X. Feng, “Large deviation for negatively dependent random variables under sublinear expectation”, Commun. Stat., Theory Methods, 45:2 (2016), 400–412 | DOI | Zbl
[3] 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 | Zbl
[4] Z. Chen, J. Xiong, “Large deviation principle for diffusion processes under a sublinear expectation”, Sci. China Math., 55:11 (2012), 2205–2216 | DOI | Zbl
[5] A. Dembo, O. Zeitouni, Large deviations techniques and applications, Applications of Mathematics, 38, 2nd ed., Springer, New York, 1998 | Zbl
[6] J.-D. Deuschel, D.W. Stroock, Large deviations, Academic Press, Inc, Boston, 1989 | Zbl
[7] F. Gao, H. Jiang, “Large deviations for stochastic differential equations driven by G-Brownian motion”, Stochastic Processes Appl., 120:11 (2010), 2212–2240 | DOI | Zbl
[8] F. Gao, M. Xu, “Large deviations and moderate deviations for independent random variables under sublinear expectations”, Scientia Sinica, 41:4 (2011), 337–352
[9] F. Hu, “On Cram$\acute{e}$r's theorem for capacities”, C. R., Math., Acad. Sci. Paris, 348:17–18 (2010), 1009–1013 | Zbl
[10] S. Peng, “Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation”, Stochastic Processes Appl., 118:12 (2008), 2223–2253 | DOI | Zbl
[11] S. Peng, “A New Central Limit Theorem under Sublinear Expectations”, Mathematics, 53:8 (2008), 1989–1994
[12] S. Peng, “G-expectation, G-Brownian motion and related stochastic calculus of It$\hat{o}$l type”, Stochastic analysis and applications, The Abel symposium 2005 Proceedings of the second Abel symposium, in honor of Kiyosi It$\hat{o}$ (Oslo, Norway, July 29–August 4, 2005), eds. Benth, Fred Espen et al., Springer, Berlin, 2007 | Zbl
[13] S. Peng, “Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations”, Sci. China Ser. A, 52:7 (2009), 1391–1411 | DOI | Zbl
[14] S. Peng, Nonlinear expectations and stochastic calculus under uncertainty, 2010, arXiv: 1002.4546v1
[15] Y. Tan, G. Zong, “Large deviation principle for random variables under sublinear expectations on $R^d$”, J. Math. Anal. Appl., 488:2 (2020), 124110 | DOI | Zbl