A Study on the Hájek-rényi Inequality and Its Applications
نویسنده
چکیده
Inequalities are at the heart of mathematical and statistical theory. No inequality is completely perfect, but the Hájek-Rényi inequality, which is the main subject of this thesis, is arguably the closest to absolute perfection of all the inequalities within all theories of probability. It has many applications in proving limit theorems, and examples of these are presented in this thesis. The strong law of large numbers for sequences of random variables and the strong growth rate for sums of random variables were obtained through utilizing the Hájek-Rényi inequality. This thesis will further extend and improve the proof of the strong law of large numbers. Additionally, the approach, utilizing the Hájek-Rényi inequality to prove limit theorems, is also applied to the weak law of large numbers for tail series.
منابع مشابه
A Hájek-Rényi-Type Maximal Inequality and Strong Laws of Large Numbers for Multidimensional Arrays
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