4 papers
Elephant Random Walk Conditioned to Avoid Zero
Kohki Iba, Go Tokumitsu
We investigate the long-time limit of an elephant random walk conditioned to avoid zero and show that the resulting process admits a Skorokhod-type embedding into a three-dimension…
Stable functional CLTs for scaled elephant random walks
Go Tokumitsu
We establish stable functional central limit theorems for scaled elephant random walks in the diffusive, critical, and superdiffusive cases using the martingale approach.
Functional central limit theorems for the dynamic elephant random walk
Go Tokumitsu
We prove functional central limit theorems for the dynamic elephant random walk in the and orders, by applying the martingale convergence theorem and Ka…
Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case
Go Tokumitsu, Kouji Yano
Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case w…