Stochastic differential equation applied to high frequency data arising in geophysics and other disciplines
Estimating future seismic hazards of a region constitutes an important study many scholars have shown a renewed interest in the past few decades. A good estimation of the seismic hazard in a region requires predicting the location and magnitude of future seismic events. As the knowledge of the geophysical mechanisms that drive seismic events have increased, so have the corresponding mathematical model representations. This thesis is devoted to the study of modeling geophysical data. We propose a stochastic differential equation arising on the superposition of independent Ornstein-Uhlenbeck processes driven by a Gamma process. Superposition of independent Gamma 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 by fitting the superposed Gamma Ornstein-Uhlenbeck model to high frequency data series in California and Chile.^
Tweneboah, Osei Kofi, "Stochastic differential equation applied to high frequency data arising in geophysics and other disciplines" (2015). ETD Collection for University of Texas, El Paso. AAI1600353.