Stationary Solutions of Semilinear Differential Equations Driven by Fractional Brownian Motions

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kianpour, Mojtaba | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43357 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohori Zangene, Bijan
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
Keywords:
Fractional Brownian Motion ; Stationary Solution ; Random Dynamical System ; Coupled Fixed Point ; Measurable Map ; Mixed Monotone ; Random Operator