Random Walk to Fit Power and Polynomial Functions
Guang Ming Wu, Shaomin Yan · 2025
This is one of our series of studies to use the random walk generated by the Monte Carlo simulation to fit various natural phenomena including global temperature-time, precipitation-time, stock index-time and commodity price-time profiles, as well as the trigonometric functions, sin, cos and tan. In this study, we applied the same technique to fit the power, rational and polynomial functions in a decimal form, including y = x, y = x2, y = x3, y = 1/x, y = 1/x2, y = 1/x3, y = 2x + 1, y = 3x2+ 2x + 1 and y = 4x3+ 3x2+ 2x + 1. The results show that the random walk can fit these functions when the number of steps is limited. Because these functions can easily find their counterparts in physics, so those continuous kinetics in the real world can be approximated by the discrete random values in a micro world.