Physical applications: Fractional Brownian movement applied to the particle dispersion

Fractional Brownian motion allows you to see the correlation between past data increments in a shift with respect to future increments. Through this important physical property of fractional Brownian motion, it was possible to perform an analysis of the impact of suspended particles, also known as particulate matter, on the environment, which is a worldwide concern. The particulate matter produced in a coal mine is large and can be disastrous for neighboring communities, resulting in a decrease in their health and quality of life in general. In this work we analyze a time series of the values of total suspended particles registered by the "La Jagua"monitoring station located 5 km from the coal mine complex in the municipality of "La Jagua"de Ibrírico in Colombia, we do this by using the fractional Brownian motion calculated from Hurst's coefficient to determine if there is persistence of the presence of this particulate material in the future. Initially a normality test is carried out, then the rescaled range and Hurst coefficient are computed with which it is possible to determine the increasing persistence and volatility of the series.