随机游走问题频域求解
首发时间:2020-03-04
摘要:随机游走问题是数学史上的一个著名问题,其解决答案被誉为数学史上250个里程碑式的重大发现之一。本文首先指出随机游走问题的本质是求解随机过程样本轨道位移特性,以及Polya使用概率分析方法在状态空间求解样本轨道特性的方法错误和将随机变量常返性用于样本轨道的概念错误。本文使用函数分析方法在频域求解随机游走样本轨道的位移特性,得出了醉汉不断远离原点的结论,从而推翻了Polya醉汉最终一定会返回原点的结论。
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Frequency Domain Solution of Random Walk Problem
Abstract:Random walk is a well-known mathematical problem, and its answer is praised as one of 250 milestones in the history of Mathematics. Firstly, this paper points out that the essence of random walk problem is to solve the sample path characteristics of random process, and Polya's method error in using probability theory to solve the sample path characteristics in state space, and conceptual error of using state space origin as sample path origin. In this paper, the displacement of random walk sample path is solved in frequency domain , and the conclusion that the drunk keeps away from the origin is drawn, which overturns Polya's conclusion that the drunk will eventually return to the origin.
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