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Title: Numerical analysis of random periodicity of stochastic differential equations
Author: Liu, Yu
ISNI:       0000 0004 7657 2742
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2018
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In this thesis, we discuss the numerical approximation of random periodic solutions (r.p.s.) of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to ∞ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √Δ t in the mean-square sense in Euler-Maruyama method and Δ t in the modified Milstein method. We obtain the weak convergence result in infinite horizon for the approximation of the average periodic measure.
Supervisor: Not available Sponsor: Loughborough University
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Random periodic solution ; Periodic measure ; Euler-Maruyama method ; Modified Milstein method ; Infinite horizon ; Rate of convergence ; Pull-back ; Weak convergence