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Title: Numerical approximations to the stationary solutions of stochastic differential equations
Authors: Yevik, Andrei
Keywords: Random dynamical system
Stochastic differential equations
Stochastic stationery solution
Numerical approximation
Euler’s method
Issue Date: 2011
Publisher: © Andrei Yevik
Abstract: This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the approximate stationary point converges in mean-square sense to the exact one as the time step of the numerical scheme diminishes.
Description: A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/7777
Appears in Collections:PhD Theses (Maths)

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