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

DOI:
https://doi.org/10.1090/S0002-9939-2011-10814-1

Published electronically:
February 28, 2011

MathSciNet review:
2813405

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-2011-10814-1

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