Statistical inference of stochastic differential equations driven by Gaussian noise.

摘要

The objective of this thesis is to study statistical inference of first and second order ordinary differential equations driven by continuous Gaussian noise under continuous time observations. The Gaussian process can be defined by a stochastic integral of a time-dependent triangular deterministic kernel with respect to standard Brownian motion. Especially, we do not assume the process to be Markovian nor a semimartingale. An important example for such a process is fractional Brownian motion. The thesis is focussed on (a) properties of these Gaussian processes (b) maximum likelihood estimation (c) asymptotic distribution of finite sample distribution of least squares type estimator.