Random periodic solutions of stochastic functional differential equations

2014-10-21T10:33:07Z (GMT) by Ye Luo
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.