A law of the iterated logarithm under sublinear expectations
By Zengjing Chen, Feng Hu. 2011
52 citations recorded by the source corpus.
In this paper, with the notion of independent and identically distributed (IID) random variables under sublinear expectations initiated by Peng, we develop a law of the iterated logarithm (LIL) for capacities. It turns out that our theorem is a natural extension of the Kolmogorov and the Hartman–Wintner LIL.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/b659a567fa53ddc2768d2a8ddd494536fb3471cd
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In Management Science and Operations Research
Citations in the corpus
- Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, background): “…very recently, including the central limit theorem and weak law of large numbers (cf. Peng (2008b, 2010)), the law of the iterated algorithm (cf. Chen and Hu (2014), Zhang (2015a)), the small derivation and Chung’s law of the iterated logarithm (c.f. Zhang (2015b)), the moment inequalities for…”
- Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm (2014, methodology): “led to be continuous if it satisfies (f) Continuityfrombelow: bE[Xn] ↑ Eb[X] if 0 6Xn ↑ X, where Xn,X∈ H ; (g) Continuityfromabove: bE[Xn] ↓ bE[X] if 0 6Xn ↓ X, where Xn,X∈ H . (II) A function V : F → [0,1] is called to be countably sub-additive if V [∞ n=1 An 6 X∞ n=1 V(An) ∀An ∈ F. (III) A capacit”
- Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm (2015, methodology): “Under the sub-linear expectation, the Hartman-Winter law of the iterated logarithm were recently established by Chen and Hu (2014) for bounded random variables, and large deviations were derived by Gao and Xu (2011, 2012).”