增强马尔可夫不等式与切比雪夫不等式
Enhancing Markov and Chebyshev's inequalities
AI总结：
本文利用受限均值思想在不增加假设的前提下显著改进马尔可夫不等式，并推广到切比雪夫不等式和切尔诺夫界，使高分位数下的界精度提升数百至数千倍，解决了其长期不精确的问题。
摘要：
受限均值的概念已被用于建立马尔可夫不等式的一个显著改进版本，且无需引入任何新的假设。该结果可直接推广到切比雪夫不等式和切尔诺夫界。改进后的马尔可夫不等式在最普遍和多样的情形下，对于高分位数给出的界比原始马尔可夫界精确数百倍甚至数千倍。马尔可夫不等式得益于其与模型无关的特性，而其长期存在的不精确性问题现已得到解决。从实际角度看，当现实情境中存在多个相互竞争的模型时，避免模型风险具有决定性意义。
英文摘要：
The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound. The improved Markov inequality yields a bound that is hundreds or thousands of times more accurate than the original Markov bound for high quantiles in the most prevalent and diverse situations. The Markov inequality benefits from being model-independent, and the long-standing issue of its imprecision is solved. Practically speaking, avoidance of model risk is decisive when multiple competing models are present in a real-world situation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
