1 |
Z. Chen, Strong laws of large numbers for sub-linear expectation, Sci. China Math. 59 (2016), no. 5, 945-954.
DOI
|
2 |
Z. Chen, C. Hu and G. Zong, Strong laws of large numbers for sub-linear expectation without independence, Comm. Stati.-Theory and Mathods 46 (2017), no. 15, 7529-7545.
DOI
|
3 |
Z. Chen. Z. & F. Hu, A law of the iterated logarithm under sublinear expectations, J. Financial Engineering 1 (2014), no. 2, 1450015. Available at https://doi.org/10.1142/S2345768614500159
DOI
|
4 |
Z. Chen, P. Wu & B. Li, A strong laws of large numbers for non-additive probabilities, Interna. J. Approx. Reason 54 (2013), no. 3, 365-377.
DOI
|
5 |
H. Cheng, A strong law of large numbers for sub-linear under a general moment condition, Stat. & Probab. Lett. 116 (2016), 248-258.
|
6 |
K. L. Chung, Note on some strong laws of large numbers, Amer. J. Math. 69 (1947), no. 1, 189-192.
DOI
|
7 |
C. Denis & C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, Ann. Appl. Probab. 16 (2006), 827-852.
DOI
|
8 |
I. Gilboa, Expected utility theory with purely subjective non-additive probabilities, J. Math. Econom. 16 (1987),65-68.
DOI
|
9 |
C. Hu, Strong laws of large numbers for sublinear expectation under controlled 1st moment condition, Chines Ann Math. Ser. B 39 (2019), no. 5, 791-804.
DOI
|
10 |
C. Jardas, J. Pecaric & N. Sarapa, A note on Chung's strong law of large numbers, JMAA 217 (1998), 328-334.
|
11 |
M. Marinacci, Limit laws for non-additive probabilities and their frequentist interpretation, J. Econom, Theory 84 (1999), 145-195.
DOI
|
12 |
S. Peng, G-expectation, G-Brownian motion and related stochastic calculus of Ito type. In: Benth, F. E., et al., Proceedings of the 2005 Abel Symposium. Springer, Berlin-Heidelberg, (2006), 541-567.
|
13 |
S. Peng, Law of large numbers and central limit theorem under nonlinear expectations, Probability, Uncertainty and Quantitative risk 4 (2019), no. 4, 1-8.
DOI
|
14 |
S. Peng, A new central limit theorem under sublinear expectations, J. Math. 53 (2008), no. 8, 1989-1994.
|
15 |
S. Peng, Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations, Sci. China Ser. A: Math. 52 (2009), no. 7, 1391-1411.
DOI
|
16 |
J. P. Xu & L. X. Zhang, Three series theorem for independent random variables under sub-linear expectations with applications, Acta Math. Sin., English Ser. 35 (2019), no. 2, 172-184.
DOI
|
17 |
S. Peng, Nonlinear expectations and stochastic calculus under uncertainty-with robust central limit theorem and G-Brownian motion, (2010), arXiv:1002.4546v1 [math.PR].
|
18 |
V. V. Petrov, On the strong law of large numbers, Theory Probab. Appli. 14 (1969), no. 2, 183-192.
DOI
|
19 |
V. V. Petrov, On the order of growth and sums of dependent variables, Theory Probab. Appli. 18 (1974), no. 2, 348-350.
DOI
|
20 |
Q. Y. Wu & Y. Y. Jiang, Strong law of large numbers and Chover's law of the iterated logarithm under sub-linear expectation, JMAA 460 (2018), 252-270.
|
21 |
L. X. Zhang, Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications, Sci. China Math. 59 (2016), no. 4, 751-768.
DOI
|
22 |
L. X. Zhang & J. H. Lin, Marcinkiewicz's strong law of large numbers for nonlinear expectations, Stat. & Probab. Lett. 137 (2018), 269-276.
DOI
|
23 |
L. X. Zhang, The convergencee of the sums of independent random variables under the sub-linear expectation, (2019). Available at https://arxiv.org/abs/1902.10872.
DOI
|