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Title: The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations
Authors: Zhou, Bo
Keywords: Stationary solution
Random dynamical system
Random difference equation
Scmilinear stochastic evolution equation
Coupling method
Gronwall inequality
Issue Date: 2009
Publisher: © Bo Zhou
Abstract: 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.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/14255
Appears in Collections:PhD Theses (Maths)

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