In this dissertation we obtain an e cient hybrid numerical method for the
solution of stochastic di erential equations (SDEs). Speci cally, our method
chooses between two numerical methods (Euler and Milstein) over a particular
discretization interval depending on the value of the simulated Brownian
increment driving the stochastic process. This is thus a new1 adaptive method
in the numerical analysis of stochastic di erential equation. Mauthner (1998)
and Hofmann et al (2000) have developed a general framework for adaptive
schemes for the numerical solution to SDEs, [30, 21]. The former presents
a Runge-Kutta-type method based on stepsize control while the latter considered
a one-step adaptive scheme where the method is also adapted based
on step size control. Lamba, Mattingly and Stuart, [28] considered an adaptive
Euler scheme based on controlling the drift component of the time-step
method. Here we seek to develop a hybrid algorithm that switches between
euler and milstein schemes at each time step over the entire discretization
interval, depending on the outcome of the simulated Brownian motion increment.
The bias of the hybrid scheme as well as its order of convergence is
studied. We also do a comparative analysis of the performance of the hybrid
scheme relative to the basic numerical schemes of Euler and Milstein. / Mathematical Sciences / M.Sc. (Applied Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/4238 |
| Date | 02 1900 |
| Creators | Chinemerem, Ikpe Dennis |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 electronic resource ( x, 112 leaves) |
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