Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm
By Li-Xin Zhang. 2015
85 citations recorded by the source corpus.
We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung’s law of the iterated logarithm are obtained.
Subfields: Management Information Systems, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/74fae4b701c5a7f39e9a5d586e4e858d1060c6d4
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In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, background): “…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 the maximum partial sums (cf., Zhang (2016)).”
- Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm (2014, methodology): “ction satisfying a polynomial growth condition, but ex and ex2 are not. Remark 3.7. When we prepare this paper, we establish a functional central limit by applying Theorem 3.5. One can refer to Zhang [24], where Chung’s law of the iterated logarithm is also established. 3.3 The law of the iterated l”