Stochastic differential equations applied to the study of geophysical and financial time series

This work is devoted to the study of modeling geophysical and financial time series. We propose a stochastic differential equation arising from the superposition of independent Ornstein-Uhlenbeck processes driven by a Γ(a,b) process. Superposition of independent Γ(a,b) Ornstein-Uhlenbeck processes offers analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to geophysics and finance by fitting the superposed Γ(a,b) Ornstein-Uhlenbeck model to typical geophysical and financial time series.