| 最长连续切换的长度 |
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| 引用本文： | 郝晨旭,胡泽春,马婷. 最长连续切换的长度[J]. 四川大学学报(自然科学版), 2021, 58(2): 021002-9 |
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| 作者姓名： | 郝晨旭 胡泽春 马婷 |
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| 作者单位： | 四川大学数学学院,成都610064 |
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| 基金项目： | 国家自然科学基金,高校基金 |
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| 摘 要： | 作为一类简单的数学模型，均匀硬币的独立抛掷模型在诸多领域具有广泛的应用，关于其最长连续头部长度的研究长期吸引着学者们进行研究。时至今日，仍有大量的研究致力于这个问题的推广、相关问题及其应用。在本文中，我们将研究最长连续切换的长度，给出几个极限定理。这些结果可能应用到可靠性理论、生物、质量控制、模式识别、金融等领域。
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| 关 键 词： | 最长连续头部 最长连续切换 极限定理 Borel-Cantelli引理 |
| 收稿时间： | 2020-03-02 |
| 修稿时间： | 2020-04-29 |
On the length of the longest consecutive switches |
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| HAO Chen-Xu,HU Ze-Chun and MA Ting. On the length of the longest consecutive switches[J]. Journal of Sichuan University (Natural Science Edition), 2021, 58(2): 021002-9 |
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| Authors: | HAO Chen-Xu HU Ze-Chun MA Ting |
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| Affiliation: | College of Mathematics, Sichuan University,College of Mathematics, Sichuan University,College of Mathematics, Sichuan University |
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| Abstract: | As a class of simple mathematical models, the model of tossing an unbiased coin independently has extensive applications in many fields, and the length of the longest head run has been long explored by a lot of scholars. Up to now, there is still a lot of study on the extension of this problem, related problems and their applications. In this paper, we will study the length of the longest consecutive switches, and present several limit theorems. These results might be applied to reliability theory, biology, quality control, pattern recognition, finance, etc. |
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