Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications
- 22 Downloads
In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz’s strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.
KeywordsSub-linear expectation capacity Rosenthal’s inequality Kolmogorov’s three series theorem Marcinkiewicz’s strong law of large numbers
MR(2010) Subject Classification60F15
Unable to display preview. Download preview PDF.
The authors thank the editors and referees for their careful reading and detailed comments, which have led to significant improvements of this paper.
- Peng, S. G.: G-expectation, G-Brownian motion and related stochastic calculus of Ito type. In: Proceedings of the 2005 Abel Symposium. Springer, Berlin-Heidelberg, 541–567, 2007Google Scholar
- Peng, S. G.: A new central limit theorem under sublinear expectations. ArXiv:0803.2656v1 (2008)Google Scholar