Random Walk Regression Problem in One and Two Dimensions
DOI:
https://doi.org/10.54097/dmev1s04Keywords:
Random walk; series convergence; binomial theorem; Stirling’s formula.Abstract
This paper examines the previous discoveries and research on the random walk problem, considers the practical application of random walk. This paper starts from the basic questions and conducts a more detailed study of the basic regression problem with one-dimensional and two-dimensional situations. Markov chains and Markov property are introduced, and then the method and important properties of series convergence are properly explained and demonstrated. Through the introduction of Brownian motion, the key part of the article is introduced, and the explanation and proof of Stirling's formula are carried out, then the proof of one-dimensional cases is entered, and the regression is proved by the above knowledge and deduction, and then the same idea is extended to the two-dimensional case for proof. Through the research and proof of this paper, the basic problem of random walk will be solved and well interpreted, laying the foundation for further research and development.
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