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Title: First-order numerical schemes for stochastic differential equations using coupling
Author: Alnafisah, Yousef Ali
ISNI:       0000 0004 6059 180X
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2016
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We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion matrix. We introduce and implement two couplings called the exact and approximate coupling for this scheme obtaining good agreement with the theoretical bound. Also we describe a method for non-invertibility case (Combined method) and we investigate its convergence order which will give O(h3/4 √log(h)j) under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them. In the last part of this thesis we work out the performance of the multilevel Monte Carlo method using the new scheme with the exact coupling and we compare the results with the trivial coupling for the same scheme.
Supervisor: Gyongy, Istvan ; Davie, Alexander Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: stochastic differential equations ; SDEs ; strong approximate solutions ; coupling ; combined method coupling ; Monte Carlo method