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Title: Random periodic solutions of stochastic functional differential equations
Author: Luo, Ye
ISNI:       0000 0004 5357 4892
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2014
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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 C([-r,0],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 C([0,τ],C([-r,0]L²(Ω))) and the generalized Schauder's fixed point theorem to show the existence of random periodic solutions.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Random periodic solution ; Random dynamical system ; Stochastic functional differential equation ; Pullback-convergence technique ; Coupling method ; Malliavin calculus ; Relative compactness.