非平稳随机过程样本轨道研究方法错误及纠正
首发时间:2020-01-23
摘要:随机过程是研究动态随机现象的一门学科,是其它学科研究动态随机现象的基本数学工具。本文指出了随机过程学科将概率分析方法直接用于非平稳随机过程样本轨道的研究方法错误,从而导致研究对象错位,产生了维纳过程常返性悖论、布朗运动样本轨道不可导谬误和数理金融学范式危机等一系列科学问题。本文使用函数分析方法推导出了维纳过程样本轨道位移公式,证明了布朗运动样本轨道的可导性,分析并纠正了数理金融学的研究方法错误。
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Errors and Correction of Research Methods for Sample Path of Non-stationary Stochastic Processes
Abstract:Stochastic process is a discipline that studies dynamic random phenomena, and is a basic mathematical tool for other disciplines to study dynamic random phenomena. This article points out that the random process discipline has used the probabilistic analysis method to directly study the sample path of non-stationary random processes. This has led to the dislocation of the research object, resulting in the Wiener process recurrence paradox, the differentiability fallacy of Brownian motion sample path, and the paradigm crisis of mathematical finance. In this paper, the formula of the sample path displacement of the Wiener process is derived using a function analysis method, which proves the differentiability of Brownian motion sample path, and analyzes and corrects the research method errors of mathematical finance.
Keywords: Wiener process Brownian motion stock price model
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