scholarly journals Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Uniform Convergence ◽  
Central Limit ◽  
Random Variables ◽  
Precise Asymptotics ◽  
Partial Sum ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

scholarly journals A law of the iterated logarithm for martingales

1991 ◽  
Vol 43 (2) ◽  
pp. 181-185 ◽  
Author(s):  
Michael Voit
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Upper Bound ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Using a slight generalisation of Brown's inequality, we show that for martingales the existence of a weak nonuniform bound on the rate of convergence in the central limit theorem yields the usual upper bound part of the law of the iterated logarithm.

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

scholarly journals On the estimate of the remainder term in the central limit theorem for non-equally distributed random variables

1972 ◽  
Vol 12 (4) ◽  
pp. 183-194
Author(s):  
V. Paulauskas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Random Variables ◽  
The Central Limit Theorem

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: В. Паулаускас. Оценка скорости сходимости в центральной предельной теореме для разнораспределенных слагаемых V. Paulauskas. Konvergavimo greičio įvertinimas centrinėje ribinėje teoremoje nevienodai pasiskirsčiusiems dėmenims

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