Limit theorems for elephant random walks remembering the very recent past, with applications to the Takagi-van der Waerden class functions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912555365040128 |
|---|---|
| author | Nakano, Yuzaburo Takei, Masato |
| author_facet | Nakano, Yuzaburo Takei, Masato |
| contents | We study the Takagi-van der Waerden functions $f_r (x)$, a well-known class of continuous but nowhere differentiable functions, from probabilistic point of view. As an application of elephant random walks remembering the very recent past (ERWVRP, a.k.a. symmetric correlated random walks), we obtain precise estimates for the oscillations of $f_r (x)$. We also establish a result on the necessary and sufficient condition for localization of the ERWVRP with variable step length, which can be applied to obtain a complete description of the differentiability properties of the Takagi-van der Waerden class functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit theorems for elephant random walks remembering the very recent past, with applications to the Takagi-van der Waerden class functions Nakano, Yuzaburo Takei, Masato Probability Classical Analysis and ODEs We study the Takagi-van der Waerden functions $f_r (x)$, a well-known class of continuous but nowhere differentiable functions, from probabilistic point of view. As an application of elephant random walks remembering the very recent past (ERWVRP, a.k.a. symmetric correlated random walks), we obtain precise estimates for the oscillations of $f_r (x)$. We also establish a result on the necessary and sufficient condition for localization of the ERWVRP with variable step length, which can be applied to obtain a complete description of the differentiability properties of the Takagi-van der Waerden class functions. |
| title | Limit theorems for elephant random walks remembering the very recent past, with applications to the Takagi-van der Waerden class functions |
| topic | Probability Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2505.08285 |