Tittel: Stationary Gaussian stochastic processes
Veileder: Geir-Arne Fuglstad
Sammendrag: The goal of this thesis is to present enough of the theory of stochastic processes to be able to discuss second order linear stochastic differential equations, i.e. equations of the form $$a\dot{Y}_ t + b\ddot{Y}_t+aY_t = X_t,$$ where $\{Y_t\}_{t\in \mathbb{R}}$ and $\{X_t\}_{t\in \mathbb{R}}$ are stochastic processes and $a$, $b$ and $c$ are scalars. We discuss the continuity, differentiability and probabilistic properties of the solution process in the case where $\{X_t\}_{t\in \mathbb{R}}$ is a stationary, Gaussian process.