Inverse Gaussian Ornstein-Uhlenbeck Applied to Modeling High Frequency Data
Abstract
With about 226050 estimated deaths worldwide in 2010, an earthquake is considered as one of the disasters that records a great number of deaths. This thesis develops a model for the estimation of magnitude of future seismic events. We propose a stochastic differential equation arising on the Ornstein-Uhlenbeck processes driven by IG(a,b) process. IG(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 financial stock markets by fitting the superposed IG(a,b) Ornstein-Uhlenbeck model to earthquake and financial time series.
Subject Area
Applied Mathematics|Mathematics
Recommended Citation
Kusi, Emmanuel Kofi, "Inverse Gaussian Ornstein-Uhlenbeck Applied to Modeling High Frequency Data" (2019). ETD Collection for University of Texas, El Paso. AAI22617710.
https://scholarworks.utep.edu/dissertations/AAI22617710