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

Abstract

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

The Law of the Iterated Logarithm

“…Readers are referred to article (Einmahl, 2016) for a LIL in the setting of random walk and in the setting of linear processes, please refer (Hambly et al, 2003). For LIL in the context of Bloch functions, please refer (Prztycki, 1989) and for Brownian motion, refer Qi and Yan (2018).…”