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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Law of large numbers under the nonlinear expectation


Authors: B. Yang and H. Xiao
Journal: Proc. Amer. Math. Soc. 139 (2011), 3753-3762
MSC (2010): Primary 60F05, 60G50; Secondary 60F99
Published electronically: February 28, 2011
MathSciNet review: 2813405
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Abstract: In this paper, we propose a class of nonlinear expectations induced by backward stochastic differential equations and reflected backward stochastic differential equations and prove the law of large numbers under the nonlinear expectation.


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Additional Information

B. Yang
Affiliation: School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, People’s Republic of China
Email: bingyang@sdu.edu.cn

H. Xiao
Affiliation: School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, People’s Republic of China
Email: xiao_hua@sdu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10814-1
PII: S 0002-9939(2011)10814-1
Keywords: Law of large numbers, nonlinear expectation, backward stochastic differential equation, reflected backward stochastic differential equation
Received by editor(s): May 20, 2010
Received by editor(s) in revised form: September 4, 2010
Published electronically: February 28, 2011
Additional Notes: The second author is the corresponding author and acknowledges the support of the National Nature Science Foundation of China (11001156, 11071144, 11026125), the Nature Science Foundation of Shandong Province (ZR2009AQ017), and the Independent Innovation Foundation of Shandong University (IIFSDU), China
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2011 American Mathematical Society