Principle and application of random walk simulation: Multilayer networks, predation and stock market

Abstract

Given the probabilities (which remain unchanged at each step) of travelling a certain distance in a certain direction, a random walk is a method used in probability theory to determine the likely position of a point depending on random movements. Markov processes, in which future behavior is independent of previous behavior, include random walks as an illustration. This study will mainly pay attention to three different applications of random walks in aspects of multilayer networks, predation and stock market. A real and intricate network could be solved by a mathematical equation depending on a random walk model. There are totally four different types of random walks that properly represent the motion of an animal searching for preys. Among these four types, CCRW is the best explanation for the route of a predator. Nevertheless, by analyzing the panel unit root tests, random walks fail to simulation the variability of share prices. This study promotes scholars to come up with an idea of the principle and application of random walks, and therefore realize the significance of such simulations.