The meaning of nonlinear random walk is introduced as follows:

Nonlinear random walk is a mathematical and statistical concept used to describe a system or process in time or space. random changes. Here, nonlinearity means that the change of the system is not a simple linear relationship, but may be affected by a variety of factors, such as nonlinear functions, feedback mechanisms, etc. Random walk means that this change is random, there is no fixed pattern or trend, and it is difficult to predict the future direction.

Random walk is originally a model of molecules related to "physical Brownian motion" or the movement of microscopic particles.

Now we talk too much about the random walk hypothesis, which is the most important hypothesis in mathematical finance. It connects the idea of ??efficient markets with Brownian motion in physics, and a whole set of Stochastic mathematical methods have become the cornerstone of mathematical finance.

(The mechanism studied has been widely used in stock research)? The proposal of the random walk model is closely linked to the change pattern of security prices. The earliest work using statistical methods to analyze returns was published in 1900 by Louis Bachelier, who applied the methods used to analyze gambling to stocks, bonds, futures, and options. In Bachelier's paper, his pioneering contribution was to realize that the random walk process is Brownian motion.

In 1953, when the British statistician Kendall applied time series analysis to study stock price fluctuations and tried to derive the pattern of stock price fluctuations, he came to a surprising conclusion: stock prices do not have any The pattern can be found, it is like "a drunk man walking, almost like the devil of opportunity still produces a random number every week, adds it to the current price to determine the price of the next week." That is, the stock price follows It is the random walk law.