×
Zhang, Miao; Chen, Zeng-jing

A law of large numbers under the nonlinear expectation. (English) Zbl 1337.60047

Acta Math. Appl. Sin., Engl. Ser. 31, No. 4, 953-962 (2015).
Summary: In this paper, we derive a law of large numbers under the nonlinear expectation generated by backward stochastic differential equations driven by G-Brownian motion.

Cited in 1 Document

MSC:

60F99 Limit theorems in probability theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J65 Brownian motion

Keywords:

law of large numbers; backward stochastic differential equations; nonlinear expectation; G-Brownian motion
Cite Review PDF
Full Text: DOI

References:

[1] Chen, Z., Wu, P., Li, B. A strong law of large numbers for non-additive probabilities. International Journal of Approximate Reasoning, 54(3): 365-377 (2013) · Zbl 1266.60051 · doi:10.1016/j.ijar.2012.06.002
[2] Denis, L., Hu, M., Peng, S. Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Analysis, 34(2): 139-161 (2011) · Zbl 1225.60057 · doi:10.1007/s11118-010-9185-x
[3] Gao, F. Pathwise properties and homeomorphic flows for stochastic differential equations driven by GBrownian motion. Stochastic Processes and their Applications, 119(10): 3356-3382 (2009) · Zbl 1176.60043 · doi:10.1016/j.spa.2009.05.010
[4] Gao, F., Jiang, H. Large deviations for stochastic differential equations driven by G-Brownian motion. Stochastic Processes and their Applications, 120(11): 2212-2240 (2010) · Zbl 1204.60050 · doi:10.1016/j.spa.2010.06.007
[5] Hu, F., Zhang, D. Central limit theorem for capacities. Comptes Rendus Mathematique, 348(19): 1111-1114 (2010) · Zbl 1203.60027 · doi:10.1016/j.crma.2010.07.026
[6] Hu, M., Ji, S., Peng, S., Song, Y. Backward stochastic differential equations driven by G-Brownian Motion. Stochastic Processes and their Applications, 124(1): 759-784 (2014) · Zbl 1300.60074 · doi:10.1016/j.spa.2013.09.010
[7] Hu, M., Ji, S., Peng, S., Song, Y. Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion. Stochastic Processes and their Applications, 124(2): 1170-1195 (2014) · Zbl 1300.60075 · doi:10.1016/j.spa.2013.10.009
[8] Li, M., Shi, Y. A general central limit theorem under sublinear expectations. Science China Mathematics, 53(8): 1989-1994 (2010) · Zbl 1213.60048 · doi:10.1007/s11425-010-3156-y
[9] Li, X., Peng, S. Stopping times and related Itô’s calculus with G-Brownian motion. Stochastic Processes and their Applications, 121(7): 1492-1508 (2011) · Zbl 1225.60088 · doi:10.1016/j.spa.2011.03.009
[10] Lin, Q. Local time and Tanaka formula for the G-Brownian motion. Journal of Mathematical Analysis and Applications, 398: 315-334 (2012) · Zbl 1267.60058 · doi:10.1016/j.jmaa.2012.09.001
[11] Maccheroni, F., Marinacci, M. A strong law of large numbers for capacities. Annals of probability, 1171-1178 (2005) · Zbl 1074.60041
[12] Marinacci, M. Limit laws for non-additive probabilities and their frequentist interpretation. Journal of Economic Theory, 84(2): 145-195 (1999) · Zbl 0921.90005 · doi:10.1006/jeth.1998.2479
[13] Peng, S., G-expectation, G-Brownian motion and related stochastic calculus of Itô type, 541-567 (2007), Berlin, Heidelberg · Zbl 1131.60057 · doi:10.1007/978-3-540-70847-6_25
[14] Peng, S. Nonlinear expectations and stochastic calculus under uncertainty. arXiv preprint arXiv:1002.4546 (2010)
[15] Song, Y. Uniqueness of the representation for G-martingales with finite variation. Electron. J. Probab, 17(24): 1-15 (2012) · Zbl 1244.60046
[16] Xu, J., Zhang, B. Martingale characterization of G-Brownian motion. Stochastic Processes and their Applications, 119(1): 232-248 (2009) · Zbl 1168.60024 · doi:10.1016/j.spa.2008.02.001
[17] Yang, B., Xiao, H. Law of large numbers under the nonlinear expectation. Proceedings of the American Mathematical Society, 139(10): 3753-3762 (2011) · Zbl 1230.60023 · doi:10.1090/S0002-9939-2011-10814-1
[18] Zhang, B., Xu, J., Kannan, D. Extension and Application of Itô’s Formula Under G-Framework. Stochastic Analysis and Applications, 28(2): 322-349 (2010) · Zbl 1222.60048 · doi:10.1080/07362990903546595
[19] Zhang, D., Chen, Z. Exponential stability for stochastic differential equation driven by G-Brownian motion. Applied Mathematics Letters, 25(11): 1906-1910 (2012) · Zbl 1253.60073 · doi:10.1016/j.aml.2012.02.063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.