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Title: The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations
Author: Zhou, Bo
ISNI:       0000 0004 2682 813X
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2009
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In this thesis, we study the existence of stationary solutions for two cases. One is for random difference equations. For this, we prove the existence and uniqueness of the stationary solutions in a finite-dimensional Euclidean space Rd by applying the coupling method. The other one is for semi linear stochastic evolution equations. For this case, we follows Mohammed, Zhang and Zhao [25]'s work. In an infinite-dimensional Hilbert space H, we release the Lipschitz constant restriction by using Arzela-Ascoli compactness argument. And we also weaken the globally bounded condition for F by applying forward and backward Gronwall inequality and coupling method.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Stationary solution ; Random dynamical system ; Random difference equation ; Scmilinear stochastic evolution equation ; Coupling method ; Gronwall inequality