Logical Structure Defect and Perfection of Stochastic Process Definition

• 1、Department of Precision Instrument,Tsinghua University

Abstract：This paper points out that the existing definition of stochastic process has only " genus concept" but no "specific difference " logical structure defect. The existing stochastic process definition only gives the " genus concept" of the binary function describing the stochastic process, but does not give the "species difference" that reflects the essential properties and quantitative relationship of the stochastic process, so it is impossible to accurately reveal the connotation and extension of the concept of stochastic process. . This paper makes a quantitative analysis of the random time series generated by the results of the coin tossing test, abstracts two important random essential properties and quantitative relationships, namely "zero mean" and " uncorrelation ", and uses white noise and operator to construct a The "species difference" which reflects the essential properties and quantitative relationship of random process, gives the definition of stochastic process with "genus concept" and "species difference" structure.

Keywords： randomness white noise frequency domain analysis；