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Stein’s method for the law of large numbers under sublinear expectations
1. | RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
2. | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
Peng, S. [
References:
[1] |
Denis, L., Hu, M. and Peng, S., Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths, Potential Anal., 2011, 34: 139-161.
doi: 10.1007/s11118-010-9185-x. |
[2] |
Fang, X., Peng, S., Shao, Q. and Song Y., Limit theorems with rate of convergence under sublinear expectations, Bernoulli, 2019, 25(4A): 2564-2596. |
[3] |
Hu, M., Peng S. and Song, Y., Stein type characterization for G-normal distributions, Electron. Commun. Probab., 2017, 22(24): 1-12. |
[4] |
Krylov, N. V., Nonlinear Parabolic and Elliptic Equations of the Second Order, Reidel Publishing Company, (Original Russian Version by Nauka, Moscow, 1985), 1987. |
[5] |
Krylov, N. V., On Shige Peng’s central limit theorem, Stochastic Process. Appl., 2020, 130(3): 1426-1434.
doi: 10.1016/j.spa.2019.05.005. |
[6] |
Peng, S., Law of large numbers and central limit theorem under nonlinear expectations, Probab. Uncertain. Quant. Risk, 2019, 4(4): 8. |
[7] |
Song,Y., Normal approximation by Stein’s method under sublinear expectations, Stochastic Process. Appl., 2020, 130(5): 2838-2850.
doi: 10.1016/j.spa.2019.08.005. |
show all references
References:
[1] |
Denis, L., Hu, M. and Peng, S., Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths, Potential Anal., 2011, 34: 139-161.
doi: 10.1007/s11118-010-9185-x. |
[2] |
Fang, X., Peng, S., Shao, Q. and Song Y., Limit theorems with rate of convergence under sublinear expectations, Bernoulli, 2019, 25(4A): 2564-2596. |
[3] |
Hu, M., Peng S. and Song, Y., Stein type characterization for G-normal distributions, Electron. Commun. Probab., 2017, 22(24): 1-12. |
[4] |
Krylov, N. V., Nonlinear Parabolic and Elliptic Equations of the Second Order, Reidel Publishing Company, (Original Russian Version by Nauka, Moscow, 1985), 1987. |
[5] |
Krylov, N. V., On Shige Peng’s central limit theorem, Stochastic Process. Appl., 2020, 130(3): 1426-1434.
doi: 10.1016/j.spa.2019.05.005. |
[6] |
Peng, S., Law of large numbers and central limit theorem under nonlinear expectations, Probab. Uncertain. Quant. Risk, 2019, 4(4): 8. |
[7] |
Song,Y., Normal approximation by Stein’s method under sublinear expectations, Stochastic Process. Appl., 2020, 130(5): 2838-2850.
doi: 10.1016/j.spa.2019.08.005. |
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