Abstract
<abstract><p>Let $ \{X_n, n\geq 1\} $ be a sequence of independent and identically distributed random variables in a sublinear expectation $ (\Omega, \mathcal H, {\mathbb {\widehat{E}}}) $ with a capacity $ {\mathbb V} $ under $ {\mathbb {\widehat{E}}} $. In this paper, under some suitable conditions, I show that a general form of precise asymptotics for complete convergence holds under sublinear expectation. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. The results extend some precise asymptotics for complete convergence theorems from the traditional probability space to the sublinear expectation space. The results also generalize the known results obtained by Xu and Cheng <sup>[<xref ref-type="bibr" rid="b34">34</xref>]</sup>.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference42 articles.
1. S. G. Peng, G-Expectation, G-Brownian motion and related stochastic calculus of Itô type, In: F. E. Benth, G. Di Nunno, T. Lindstrøm, B. Øksendal, T. Zhang, Stochastic analysis and applications, Abel Symposia, 2 (2007), 541–567. doi: 10.1007/978-3-540-70847-6_25.
2. L. Denis, C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, Ann. Appl. Probab., 16 (2006), 827–852. doi: 10.1214/105051606000000169.
3. I. Gilboa, Expected utility with purely subjective non-additive probabilities, J. Math. Econ., 16 (1987), 65–88. doi: 10.1016/0304-4068(87)90022-X.
4. M. Marinacci, Limit laws for non-additive probabilities and their frequentist interpretation, J. Econom. Theory, 84 (1999), 145–195. doi: 10.1006/jeth.1998.2479.
5. S. G. Peng, Backward SDE and related g-expectation, In: N. El Karoui, L. Mazliak, Backward stochastic differential equations, Pitman Research Notes in Mathematics Serie, Longman, Harlow, 364 (1997), 141–159.
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献