Yuzaburo Nakano

collaborators

3 papers

math.PR2026

An almost sure invariance principle for the Takagi-van der Waerden class functions

Yuzaburo Nakano

The Takagi-van der Waerden functions are a well-known class of continuous but nowhere differentiable functions. In this paper, we study their weighted versions, the Takagi-van der…

math.PR2025

Limit theorems for elephant random walks remembering the very recent past, with applications to the Takagi-van der Waerden class functions

Yuzaburo Nakano, Masato Takei

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…

math.PR2025

Elephant random walk with polynomially decaying steps

Yuzaburo Nakano

In this paper, we introduce a variation of the elephant random walk whose steps are polynomially decaying. At each time $k$ , the walker's step size is $k^{- I^^{3}}$ with $I^^{3} > 0$ . We inv…