Theoretical and Natural Science

- The Open Access Proceedings Series for Conferences


Theoretical and Natural Science

Vol. 13, 30 November 2023


Open Access | Article

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

Yufei Yang * 1
1 Shanghai Southwest Weiyu Middle School

* Author to whom correspondence should be addressed.

Theoretical and Natural Science, Vol. 13, 36-44
Published 30 November 2023. © 2023 The Author(s). Published by EWA Publishing
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation Yufei Yang. Principle and application of random walk simulation: Multilayer networks, predation and stock market. TNS (2023) Vol. 13: 36-44. DOI: 10.54254/2753-8818/13/20240771.

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.

Keywords

Random Walk, Markov Process, Multilayer Networks, Predation, Stock Market

References

1. Prigogine I, Stuart A R. Advances in Chemical Physics. An Interscience Publication. Unite States of America, 1983, 2: 364.

2. Reid G A. The Causation of Variations. Nature, 1905, 72(1866): 318-319.

3. George H. Weiss. Random Walks and Their Applications: Widely used as mathematical models, random walks play an important role in several areas of physics, chemistry, and biology. American Scientists, 1983, 71: 65-71.

4. Enrico S. The application of continuous-time random walks in finance and economics. Physica A, 2005: 233.

5. Haji-Sheikh A, Sparrow E M. The Floating Random Walk and its Application to Monte Carlo Solutions of Heat Equations. J. SIAM Appl. Math., 1966, 14: 371.

6. Boris P B, David A Z. Analysis of a one-dimensional random walk with irreversible losses at each step: applications for protein movement on DNA. Journal of Theoretical Biology, 2003, 11: 195.

7. Rozanov Y A. Probability Theory: A Concise Course. Dover Publications, Inc. New York, 1997: 87-88.

8. Gregory F L, Vlada L. Random Walk: A Modern Introduction. Cambridge University Press, London, 2010.

9. Frank S. Principles of Random Walk. Springer Verlag. New York, 1964.

10. Li X, Xu G, Tang M. Community detection for multilayer social network based on local random walk. J. Vis. Commun, Image R., 2018, 11: 91.

11. Lucas G S J, Michael W M, Peter J M, Mason A P. A local perspective on community structure in multilayer networks. Network Science, 2017: 1.

12. Albert S R, Manlio De, Sergio G, Alex A. Random walk centrality in interconnected multilayer networks. Physica D, 2016, 23: 74-77.

13. Cristina D, Giuseppe O, Vito T. Random Walks in Swarm Robotics: An Experiment with Kilobots. Swarm Intelligence, 2016, 9882: 185.

14. Maria S, Aljaz G, Gleb O, Ralf M. A single predator charging a herd of prey: effects of self volume and predator-prey decision-making. Journal of Physics A: Mathematical and Theoretical, 2016, 11: 2.

15. Bläßle A, Tyson R C. First capture success in two dimensions: The search for prey by a random walk predator in a comprehensive space of random walks. Ecological Complexity, 2016, 13: 24-26.

16. Jamshedpur J. Random walk model and symmetric effect in Korean composite stock price index. Afro-Asian J. Finance and Accounting, 2018, 8: 85.

17. Ahmed R S, Emran H. Testing Weak Form of Market Efficiency of DSE Based on Random Walk Hypothesis Model: A Parametric Test Approach. International Journal of Accounting and Financial Reporting, 2019, 9: 400.

18. Dilek D C, Serdar I, Dundar K. Do stock markets follow a random walk? New Evidence for an old question. International Review of Economics and Finance, 2019, 165: 172-173.

Data Availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Authors who publish this series agree to the following terms:

1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this series.

2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this series.

3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See Open Access Instruction).

Volume Title
Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
ISBN (Print)
978-1-83558-189-6
ISBN (Online)
978-1-83558-190-2
Published Date
30 November 2023
Series
Theoretical and Natural Science
ISSN (Print)
2753-8818
ISSN (Online)
2753-8826
DOI
10.54254/2753-8818/13/20240771
Copyright
30 November 2023
Open Access
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Copyright © 2023 EWA Publishing. Unless Otherwise Stated