Brownian motion hypothesis is the core hypothesis of modern capital market theory. Modern capital market theory holds that the prices of securities and futures are stochastic. The so-called randomness here refers to the memoryless of data, that is, past data does not form the basis for predicting future data. At the same time, there will be no strikingly similar repetition. The mathematical definition of random phenomenon is: in individual experiments, the results are uncertain; In a large number of repeated experiments, the results have statistical regularity. Wiener process describing Brownian motion, one of the stock price behavior models, is a special form of Markov random process. Markov process is a special type of stochastic process. Stochastic process is a probability model based on probability space, which is regarded as the dynamics of probability theory, that is, its research object is random phenomena that evolve with time. So random behavior is a kind of behavior with statistical regularity. The stock price behavior model is usually expressed by the famous Wiener process. It is tempting to assume that the stock price follows the generalized Wiener process, that is, it has constant expected drift rate and variance rate. Wiener process shows that only the current value of variables is related to future prediction, while the past history of variables and the evolution mode of variables from the past to the present are not related to future prediction. The Markov property of stock price is consistent with the weak form of market efficiency, that is to say, the current price of a stock already contains all the information, including of course all the past price records. However, when people began to study the financial market with fractal theory, they found that its operation did not follow Brownian motion, but obeyed the more general geometric Brownian motion.