The next equation of motion is a differential equation, which shows -Option pricing model-caliculation, shows behavior of the stock price X at time t on the assumption that stock prices rely on the winner process.

It deals with a pricing model on the assumption that δ in the market fluctuates by random. Uncertain behavior of the stock price shows following equation.

This model has a property of a time series change for a parameter standard deviation depends on historical samples. This model includes the property that once the market change in large scale then the large fluctuation tends to continue after that. The shape of the market price changes is a fat tail and it approximates the real world market behavior than normal distribution.