随机过程理论的范式危机与变革
首发时间:2020-07-03
摘要:本文首先分析了随机过程理论中布朗运动样本轨道性质与经验事实不符、在逻辑上不能自洽而出现悖论、与物理学理论不一致,以及在金融市场的广泛应用导致金融危机等反常问题,并指出将样本轨道抽象为随机变量的研究方法导致研究对象错位是随机过程理论产生范式危机的根本原因。随机过程理论必须要进行全面的范式变革,摒弃将样本轨道当作随机变量的错误范式,并用时间函数范式重建样本轨道理论,这样才能正确揭示随机现象随时间的演变规律。
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Paradigm Crisis and Paradigm shift of Stochastic Process
Abstract:This article first analyzes the abnormal problems such as the inconsistency between the sample path properties of the stochastic process theory and the empirical facts, paradox caused by logical incoherence, inconsistent with physics theory, and the financial crisis caused by the widespread application in the financial market, and points out that the research method of treating the sample path as a random variable leads to the dislocation of the research object is the fundamental reason for the paradigm crisis of the stochastic process theory. It is necessary to carry out a comprehensive paradigm shift on the theory of stochastic process, abandon the wrong paradigm that regards the sample path as a random variable, and reconstruct the sample path theory with time function paradigm, so as to correctly reveal the evolution law of random phenomenon with time.
Keywords: stochastic processes paradigm crisis paradigm shift
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