Welschinger, M. Lilian (2024) La marche aléatoire de l’éléphant PRE - Research Project, ENSTA.
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Abstract
The elephant random walk is a stochastic process characterized by a memory para- meter, meaning that future movements depend on past displacements. I will study the recurrence and transience properties of this walk, as well as various asymptotic results. Additionally, I will analyze several lower bounds for this walk to better understand its long-term behavior. We will also explore the connections this walk may have with bran- ching processes and Pólya urns but also how the use of martingales enables us to obtain results. This research will highlight fundamental aspects of this stochastic processe.
Item Type: | Thesis (PRE - Research Project) |
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Uncontrolled Keywords: | Random walk, recurrence, transience, Pólya urns, martingale. |
Subjects: | Mathematics and Applications |
ID Code: | 10128 |
Deposited By: | Lilian WELSCHINGER |
Deposited On: | 28 août 2024 16:38 |
Dernière modification: | 28 août 2024 16:38 |
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