Analysis of the Principle and Applications of Random Walk: Finance, Diffusion Equations and Game Design

As a matter of fact, as a common simulation types, random walk is widely applied in various fields in recent years incorporating with the Monte-Carlo simulations. With this in mind, this study summarizes and provides an analysis of the principle and applications of random walks in three diverse fields, i.e., finance, game strategy, and game design. To be specific, it begins by introducing the historical background and significance of random walk research as well as the basic mathematical descriptions. Recent advancements and applications of random walks are discussed. In reality, the analysis includes an explanation of the basic concepts and mathematical representations of random walks, followed by three specific applications with real-world scenarios and results. At the same time, the study also discusses the limitations of current random walk applications and offers insights into future research prospects. Overall, these results shed light on guiding further exploration of random walk applications.