Stationary Solutions of Semilinear Differential Equations Driven by Fractional Brownian Motions, M.Sc. Thesis Sharif University of Technology ; Zohori Zangene, Bijan (Supervisor)
Abstract
Let (X; d) be a metric space and (X;) be a partially ordered Space. Let F, g be measurable mappings such that F has g-monotone property and satisfying in a contraction condition. Firstly, some extentions of Banach fixed point theorem was investigated in particular way that lead to random coupled and random fixed point for mentioned mappings. Then, linear stochastic evolution equation and semilinear dissipitive stochastic evolution equation driven by infinite dimentional fractional Brownian noise was evaluated. It has been shown these equations define random dynamical systems with exponentially attracting random fixed points that are stationary solution for them
Cataloging briefStationary Solutions of Semilinear Differential Equations Driven by Fractional Brownian Motions, M.Sc. Thesis Sharif University of Technology ; Zohori Zangene, Bijan (Supervisor)
Abstract
Let (X; d) be a metric space and (X;) be a partially ordered Space. Let F, g be measurable mappings such that F has g-monotone property and satisfying in a contraction condition. Firstly, some extentions of Banach fixed point theorem was investigated in particular way that lead to random coupled and random fixed point for mentioned mappings. Then, linear stochastic evolution equation and semilinear dissipitive stochastic evolution equation driven by infinite dimentional fractional Brownian noise was evaluated. It has been shown these equations define random dynamical systems with exponentially attracting random fixed points that are stationary solution for them
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