一维简单随机游走常返性证伪
首发时间:2020-04-09
摘要:一维简单随机游走是一种具有离散时间参数和离散状态空间的基本随机过程。本文从一维简单随机游走的常返性推导出了一维简单随机游走的方差与中心极限定理相悖的结论,从而证明了一维简单随机游走的常返性不能成立。本文依据一维简单随机游走定义和大数定律,推导出了一维简单随机游走样本轨道的位移公式和自相关函数,得出了一维简单随机游走的位移与时间成正比的结论,从而推翻了波利亚随机游走定理,并纠正了喝醉的酒鬼最终会返回原点的谬误。
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Disproving the recurrence of one-dimensional simple random walk
Abstract:One-dimensional simple random walk is a basic random process with discrete time parameters and discrete state space. This paper derives the conclusion that the variance of the one-dimensional simple random walk is contrary to the Central Limit Theorem from the recurrence of the one-dimensional simple random walk, thus proving that the recurrence of the one-dimensional simple random walk cannot be established. Based on the definition of the one-dimensional simple random walk and the Law of Large Numbers, this paper derives the displacement formula and autocorrelation function of the sample path of one-dimensional simple random walk. The displacement of one-dimensional simple random walk is proportional to time. This conclusion overturned Polya\'s random walk theorem and correctedthe fallacy that a drunk man will eventually find his way home.
Keywords: Markov process Random Walk Recurrence
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