\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level crossing findings more sense. In this article, we calculated the average frequency of upcrossing for a wide range of fractional Gaussian noises from logarithmic (zero Hurst exponent, H=0), to Gaussian, H=1, ($0