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)
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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