Ergodic properties of fractional-driven stochastic differential equations and their applications
File(s)
Author(s)
Sieber, Julian
Type
Thesis
Abstract
This dissertation presents our research on the following problems in the asymptotic theory of dynamics driven by fractional noise: We derive regularity properties of the stationary density of stochastic differential equations driven by additive fractional Brownian motion. We prove a geometric rate of convergence of the law of the solution to fractional-driven stochastic differential equations to the stationary distribution. This improves previously known results which obtained algebraic and sub-exponential rates. We establish an averaging principle for slow-fast systems for which both motions are driven by fractional Brownian motions. We obtain an averaging principle for semi-linear stochastic differential equations driven by cylindrical fractional Brownian motion. We show a functional central limit theorem for non-autonomous ordinary differential equations in a random environment modeled by a fractional Ornstein-Uhlenbeck process.
Version
Open Access
Date Issued
2023-07
Date Awarded
2023-12
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Hairer, Xue-Mei
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)