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Title: Numerical approximations to the stationary solutions of stochastic differential equations
Author: Yevik, Andrei
ISNI:       0000 0004 2718 2449
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2011
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Random dynamical system ; Stochastic differential equation ; Stochastic stationery solution ; Numerical approximation ; Euler’s method