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