Abstract
Exponential rate is the best in convergence in probability. Such inequalities are important when investigating the law of large numbers and the law of iterated logarithm. Some of such inequalities are well known and frequently employed in statistics and probability, such as Hoeffding, Bernstein, Bennett and Kolmogorov inequalities. These inequalities can be found in most textbooks on limiting theorems, such as (1977), (1995). Some new inequalities will be referenced therein.
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Lin, Z., Bai, Z. (2010). Exponential Type Estimates of Probabilities. In: Probability Inequalities. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05261-3_7
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DOI: https://doi.org/10.1007/978-3-642-05261-3_7
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