Thesis-2011-Yevik.pdf (1.11 MB)

Numerical approximations to the stationary solutions of stochastic differential equations

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thesis
posted on 19.01.2011, 09:32 by Andrei Yevik
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.

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

© Andrei Yevik

Publication date

2011

Notes

A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.

EThOS Persistent ID

uk.bl.ethos.551266

Language

en

Exports