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Hybrid numerical methods for stochastic differential equations

Show simple item record Chinemerem, Ikpe Dennis 2011-05-26T07:12:44Z 2011-05-26T07:12:44Z 2009-02
dc.description.abstract 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. en
dc.format.extent 1 electronic resource ( x, 112 leaves)
dc.language.iso en en
dc.subject.ddc 515.35
dc.subject.lcsh Stochastic differential equations
dc.subject.lcsh Numerical analysis
dc.subject.lcsh Integral equations -- Numerical solutions
dc.title Hybrid numerical methods for stochastic differential equations en
dc.type Dissertation en
dc.description.department Mathematical Sciences M.Sc. (Applied Mathematics)

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