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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 solution
Random dynamical system
Stochastic functional differential equation
Pullback-convergence technique
Coupling method
Malliavin calculus
Relative 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)

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