View Submission - EcoSta2019

A0515
**Title: **Weak convergence of the partial sum of $I(d)$ process to a fractional Brownian motion in finite interval representation
**Authors: **Junichi Hirukawa - Niigata University (Japan) **[presenting]**

Kou Fujimori - Waseda University (Japan)

**Abstract: **An integral transformation which changes a fractional Brownian motion to a process with independent increments has been given. A representation of a fractional Brownian motion through a standard Brownian motion on a finite interval has also been given. On the other hand, it is known that the partial sum of the discrete time fractionally integrated process ($I(d)$ process) weakly converges to a fractional Brownian motion in infinite interval representation. We derive the weak convergence of the partial sum of $I(d)$ process to a fractional Brownian motion in finite interval representation.

Kou Fujimori - Waseda University (Japan)