Translator Disclaimer
2020 $L^{p}$ uniform random walk-type approximation for Fractional Brownian motion with Hurst exponent $0 < H < \frac {1}{2}$
Alberto Ohashi, Francys A. de Souza
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP367

Abstract

In this note, we prove an $L^{p}$ uniform approximation of the fractional Brownian motion with Hurst exponent $0 < H < \frac {1}{2}$ by means of a family of continuous-time random walks imbedded on a given Brownian motion. The approximation is constructed via a pathwise representation of the fractional Brownian motion in terms of a standard Brownian motion. For an arbitrary choice $\epsilon _{k}$ for the size of the jumps of the family of random walks, the rate of convergence of the approximation scheme is $O(\epsilon _{k}^{p(1-2\lambda )+ 2(\delta -1)})$ whenever $\max \{0,1-\frac {pH}{2}\}< \delta < 1$, $\lambda \in \big (\frac {1-H}{2}, \frac {1}{2} + \frac {\delta -1}{p}\big )$.

Citation

Download Citation

Alberto Ohashi. Francys A. de Souza. "$L^{p}$ uniform random walk-type approximation for Fractional Brownian motion with Hurst exponent $0 < H < \frac {1}{2}$." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP367

Information

Received: 18 August 2020; Accepted: 15 December 2020; Published: 2020
First available in Project Euclid: 31 December 2020

Digital Object Identifier: 10.1214/20-ECP367

Subjects:
Primary: 60G15
Secondary: 60G18

JOURNAL ARTICLE
13 PAGES


SHARE
Back to Top