Thesis-2014-Luo.pdf (657.87 kB)
Random periodic solutions of stochastic functional differential equations
thesis
posted on 2014-10-21, 10:33 authored by Ye LuoIn this thesis, we study the existence of random periodic solutions for both nonlinear dissipative stochastic functional differential equations (SFDEs) and semilinear nondissipative SFDEs in $\mathcal{C}([-r,0],\mathbb{R}^d)$. Under some sufficient conditions for the existence of global semiflows for SFDEs, by using pullback-convergence technique to SFDE, we obtain a general theorem about the existence of random periodic solutions. By applying coupled forward-backward infinite horizon integral equations method, we perform the argument of the relative compactness of Wiener-Sobolev spaces in $\mathcal{C}([0,\tau], \mathcal{C}([-r,0], \mathbf{L}^2 (\Omega)))$ and the generalized Schauder's fixed point theorem to show the existence of random periodic solutions.
Funding
none
History
School
- Science
Department
- Mathematical Sciences
Publisher
© Ye LuoPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2014Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.EThOS Persistent ID
uk.bl.ethos.631608Language
- en