Random walk theory and application
Mathematics Department, University of Benin, Nigeria.
Research Article
World Journal of Advanced Engineering Technology and Sciences, 2024, 11(02), 346–367.
Article DOI: 10.30574/wjaets.2024.11.2.0116
Publication history:
Received on 23 February 2024; revised on 01 April 2024; accepted on 04 April 2024
Abstract:
This project presents an overview of Random Walk Theory and its applications, as discussed in the provided project work. Random Walk Theory posits that changes in elements like stock prices follow a distribution independent of past movements, making future predictions challenging. Originating from the work of French mathematician Louis Bachelier and later popularized by economist Burton Markiel, the theory finds extensive applications beyond finance, spanning fields such as psychology, economics, and physics. The project delves into various types of random walks, including symmetric random walks, and explores their implications in different spaces, from graphs to higher-dimensional vector spaces. It provides definitions, examples, and graphical representations to elucidate random walk concepts, highlighting their relevance in practical scenarios like particle movement and stock price fluctuations. Key concepts such as the reflection principle and the main lemma are discussed to provide a comprehensive understanding of random walks and their properties. Through examples and lemmas, the project elucidates the mathematical foundations of random walks, offering insights into their behavior and applications across diverse disciplines. In summary, this project contributes to a deeper comprehension of Random Walk Theory, serving as a fundamental framework for understanding stochastic processes and their real-world implications.
Keywords:
Random Walk Theory; Application; Project; Elements
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Copyright © 2024 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0