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22 April 2022 Simple random walk and Pólya’s recurrence theorem
Purui Xu
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Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121630N (2022) https://doi.org/10.1117/12.2628024
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China
Abstract
The essay puts focus on the properties of the random walk, especially the simple random walk. In the properties, recurrence and transience is the most important one to cover with the comprehensive deduction from Pólya random walk theorem. Moreover, simulation in one- and two-dimension in python is used to verify it, and the essay finally gets a more straightforward statement of this theorem.
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Purui Xu "Simple random walk and Pólya’s recurrence theorem", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121630N (22 April 2022); https://doi.org/10.1117/12.2628024
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KEYWORDS
Statistical analysis
Motion models
Particles
Computer simulations
Mathematical modeling
Probability theory
Stochastic processes
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