A law of iterated logarithm for the subfractional Brownian motion and an application

Hongsheng Qi; Litan Yan

doi:10.1186/s13660-018-1675-1

A law of iterated logarithm for the subfractional Brownian motion and an application

J Inequal Appl. 2018;2018(1):96. doi: 10.1186/s13660-018-1675-1. Epub 2018 Apr 23.

Authors

Hongsheng Qi¹, Litan Yan²

Affiliations

¹ Department of Mathematics, College of Science, Bengbu University, Bengbu, P.R. China.
² 2Department of Mathematics, College of Science, Donghua University, Shanghai, P.R. China.

Abstract

Let [Formula: see text] be a sub-fractional Brownian motion with Hurst index [Formula: see text]. In this paper, we give a local law of the iterated logarithm of the form [Formula: see text] almost surely, for all [Formula: see text], where [Formula: see text] for [Formula: see text]. As an application, we introduce the [Formula: see text]-variation of [Formula: see text] driven by [Formula: see text] [Formula: see text] with [Formula: see text].

Keywords: Iterated logarithm; Sub-fractional Brownian motion; Φ-variation.