@article{TVP_2020_65_4_a6,
author = {Q. Zhou and A. I. Sakhanenko and J. Guo},
title = {Prokhorov distance with rates of convergence under sublinear expectations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {778--804},
year = {2020},
volume = {65},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a6/}
}
TY - JOUR AU - Q. Zhou AU - A. I. Sakhanenko AU - J. Guo TI - Prokhorov distance with rates of convergence under sublinear expectations JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2020 SP - 778 EP - 804 VL - 65 IS - 4 UR - http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a6/ LA - ru ID - TVP_2020_65_4_a6 ER -
Q. Zhou; A. I. Sakhanenko; J. Guo. Prokhorov distance with rates of convergence under sublinear expectations. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 778-804. http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a6/
[1] A. A. Borovkov, “On the rate of convergence for the invariance principle”, Theory Probab. Appl., 18:2 (1974), 207–225 | DOI | MR | Zbl
[2] M. D. Donsker, “An invariance principle for certain probability limit theorems”, Four papers on probability, Mem. Amer. Math. Soc., 6, Amer. Math. Soc., Providence, RI, 1951, 12 pp. | MR | Zbl
[3] Xiao Fang, Shige Peng, Qi-man Shao, Yongsheng Song, “Limit theorems with rate of convergence under sublinear expectations”, Bernoulli, 25:4A (2019), 2564–2596 ; arXiv: 1711.10649v1 | DOI | MR | Zbl
[4] Shige Peng, “Nonlinear expectations and nonlinear Markov chains”, Chinese Ann. Math. Ser. B, 26:2 (2005), 159–184 | DOI | MR | Zbl
[5] Shige Peng, “$G$-expectation, $G$-Brownian motion and related stochastic calculus of Itô type”, Stochastic analysis and applications, Abel Symp., 2, Springer, Berlin, 2007, 541–567 | DOI | MR | Zbl
[6] Min Li, Yufeng Shi, “A general central limit theorem under sublinear expectations”, Sci. China Math., 53:8 (2010), 1989–1994 | DOI | MR | Zbl
[7] Shige Peng, Nonlinear expectations and stochastic calculus under uncertainty. With robust CLT and G-Brownian motion, Probab. Theory Stoch. Model., 95, Springer, Berlin, 2019, xiii+212 pp. ; arXiv: 1002.4546v1 | DOI | MR | Zbl
[8] Yu. V. Prokhorov, “Convergence of random processes and limit theorems in probability theory”, Theory Probab. Appl., 1:2 (1956), 157–214 | DOI | MR | Zbl
[9] A. I. Sakhanenko, “Simple method of obtaining estimates in the invariance principle”, Probability theory and mathematical statistics (Kyoto, 1986), Lecture Notes in Math., 1299, Springer, Berlin, 1988, 430–443 | DOI | MR | Zbl
[10] A. I. Sakhanenko, “On the accuracy of normal approximation in the invariance principle”, Siberian Adv. Math., 1:4 (1991), 58–91 | MR | MR | Zbl
[11] A. I. Sakhanenko, “A new way to obtain estimates in the invariance principle”, High dimensional probability II (Seattle, WA, 1999), Progr. Probab., 47, Birkhäuser Boston, Boston, MA, 2000, 223–245 | DOI | MR | Zbl
[12] A. I. Sakhanenko, “Estimates in the invariance principle in terms of truncated power moments”, Siberian Math. J., 47:6 (2006), 1113–1127 | DOI | MR | Zbl
[13] V. V. Jurinskii, “A smoothing inequality for estimates of the Lévy–Prokhorov distance”, Theory Probab. Appl., 20:1 (1975), 1–10 | DOI | MR | Zbl