Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171

# Loughborough University Institutional Repository

 Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/16112

 Title: Random periodic solutions of stochastic functional differential equations Authors: Luo, Ye Keywords: Random periodic solutionRandom dynamical systemStochastic functional differential equationPullback-convergence techniqueCoupling methodMalliavin calculusRelative compactness. Issue Date: 2014 Publisher: © Ye Luo Abstract: In 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. Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University. Sponsor: none Version: Not specified URI: https://dspace.lboro.ac.uk/2134/16112 Appears in Collections: PhD Theses (Maths)

Files associated with this item:

File Description SizeFormat