ABSTRACT

Simple 1D random walk is modeled by random steps to the left or to the right on the x-axis. The interpolation is not a proper method for random data because randomness means that some pairs represent the dependence f with small probability. The method of Monte Carlo is a simulation method based on the realizations of random variables. The independent papers by Albert Einstein and by Marian Smoluchowski can be considered as a rigorous demonstration of Brownian motion based on the diffusion equation and random walks. A formal mathematical introduction to the theory of discrete random variables can be found. If a theory works in one domain, it can be applied in another one by analogy.