# On the laws of the iterated logarithm under the sub-linear expectations without the assumption on the continuity of capacities

@inproceedings{Zhang2021OnTL, title={On the laws of the iterated logarithm under the sub-linear expectations without the assumption on the continuity of capacities}, author={Li-Xin Zhang}, year={2021} }

In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential inequalities for the maximum sum of independent random variables and Kolmogorov’s converse exponential inequalities are established as tools for showing the law of the iterated logarithm. As an application, the sufficient and necessary conditions of the law of…

## References

SHOWING 1-10 OF 27 REFERENCES

Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm

- Mathematics
- 2014

Kolmogorov’s exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables.…

The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations

- Mathematics
- 2019

Let { X n ; n ≥ 1} be a sequence of independent random variables on a probability space (Ω ,F ,P) and $${S_n} = \sum\nolimits_{k = 1}^n {{X_k}} $$ . It is well-known that the almost sure convergence,…

On the Law of the Iterated Logarithm for Independent Banach Space Valued Random Variables

- Mathematics
- 1993

In this paper we establish some general forms of the law of the iterated logarithm for independent random variables (Xn) with Banach space values, where (Xn) is not necessarily identically…

On Almost Sure Convergence

- Mathematics
- 1951

Since the discovery by Borel1 (1907) of the strong law of large numbers in the Bernoulli case, there has been much investigation of the problem of almost sure convergence and almost sure summability…

Probability Inequalities for Sums of Independent Random Variables

- Mathematics
- 1971

where x > 0, y > O,A EIXI < ,t > 2andK 1 + e-t(t + 1)t+2. This paper is devoted to improving this result and to extending it to the case of non-identically distributed independent random variables…

Lindeberg’s central limit theorems for martingale like sequences under sub-linear expectations

- Mathematics
- 2016

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes, especially stochastic integrals and differential equations. In this paper, the…

A hypothesis-testing perspective on the G-normal distribution theory

- Mathematics
- 2019

The G-normal distribution was introduced by Peng [2007] as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution…

Sufficient moment and truncated moment conditions for the law of the iterated logarithm

- Mathematics
- 1987

SummaryVarious sufficient conditions for the law of the iterated logarithm are given extending the main result of the author's previous paper [16] and Kolmogoroff's law of iterated logarithm. As a…

A New Central Limit Theorem under Sublinear Expectations

- Mathematics
- 2008

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our…

General One-Sided Laws of the Iterated Logarithm

- Mathematics
- 1981

Let $\{X_i\}$ be a sequence of independent, identically distributed nondegenerate random variables and $S_n = \sum^n_{i = 1}X_i$. We consider the question for various centering sequences…